A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.
Answers
cos(t)=-15/17
tan(t)=-8/15
sec(t)=-17/15
csc(t)=17/8
cot(t)=-15/8
Point P is on the unit circle U. The values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
Given:
From the given figure, the coordinate of point P is [tex](-\dfrac{15}{17}, \dfrac{8}{17})[/tex].
The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be [tex](x,y)\equiv (cos\theta, sin\theta)[/tex].
By comparing the given coordinate with the general expression, the value sine and cosine function will be,
[tex]sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}[/tex]
Now, the other trigonometric functions will be,
[tex]tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}[/tex]
Therefore, the values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].
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Related Questions
Kristen owns a bakery called Kristen’s cakes and such and is considering lowering the price of her cakes Kristen pulls her customers and determines that she can sell 100 cakes each week when she charges $25 each she also discovers that for every one dollar decrease in the price of the cake she will sell five more cakes the graph below represents Christians projected weekly revenue for each decrease in the price at what price she Christian sell her cakes in order to meet her maximum potential revenue
Answers
Jen picked 3/4 of a gallon of strawberries in half an hour. If she keeps picking strawberries at the same rate, how many gallons will she have picked in 2 hours.
Answers
3/4 = 0.75 as a decimal
We know that Jen picks 0.75 of a gallon of strawberries in half an hour, and now we want to find out how many gallons she'll pick in 2 hours.
Half an hour = 0.5 2 ÷ 0.5 = 4 There are four half hours in 2 hours.
0.75 × 4 = 3
ANSWER:
Jen will have picked 3 gallons of strawberries in 2 hours.
Classify each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
-2x^2-x+3.5
10xyz^3
-x^2y^2+2y
8x^2+0.25
x^3y^4+2x^2y-3z
Answers
Answer:
it is 10xyz^3 for monomial. 8x^2+0.25 and -x^2y^2+2y for binomial. And -2x^2-x+3.5 and x^3y^4+2x^2y-3z for trinomial.
Step-by-step explanation:
[tex]10xyz^3[/tex] for monomial. [tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex] for binomial. And [tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex] for trinomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We need to find each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
Therefore,
If there is one term, the polynomial will be called monomial thus;
[tex]10xyz^3[/tex]
If there are two terms, the polynomial will be called binomial thus;
[tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex]
If there are three terms, the polynomial will be called trinomial thus;
[tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex]
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The sum of the first and second of three consecutive even integers is 158. find the three even integers.
Answers
The length of a rectangular park is 20 feet longer than the width of the park. If the length of the park is 36 feet, what is the width of the park? 4 feet 16 feet 42 feet 56 feet
Answers
A radius is an angle that connects any point on the circle to the center of that circle. A. True B. False
Answers
Answer:
IT REALLY IS FALSE FOREHEADS
Step-by-step explanation:
Seventy-five bottles of water are randomly tested from the large inventory in a warehouse. Which term refers to the large inventory of water bottles in the warehouse
Answers
When cyclist squeezes her brake lever, she can stop with an acceleration of -3.0 m/s^2 how far will her bike travel while coming to a complete stop if her initial speed was 11 m/s
Answers
v² = u² + 2as
where
v = final speed. v = 0 because the cyclist comes to a complete stop.
u = initial speed. u = 11 m/s, given
a = acceleration. a = -3.0 m/s², given
s = distance traveled, m.
Therefore
0 = 11² + 2(-3.0)*s
0 = 121 - 6s
That is,
6s = 121
s = 121/6 = 20.167 m
Answer: 20.2 m (nearest tenth)
Final answer:
The cyclist will travel approximately 20.17 meters before coming to a complete stop when decelerating with an acceleration of [tex]-3.0 m/s^2[/tex] from an initial speed of 11 m/s.
Explanation:
To calculate the distance the cyclist's bike will travel while coming to a complete stop with an initial speed of 11 m/s and an acceleration of [tex]-3.0 m/s^2[/tex], we can use one of the equations of motion. Specifically, we need to use the equation [tex]v^2 = u2 + 2as[/tex], where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
In this case, the final velocity v = 0 m/s (because the bike comes to a stop), the initial velocity u = 11 m/s, and the acceleration a = [tex]-3 m/s^2[/tex] (the negative sign indicates that it is a deceleration).
Plugging these values into the equation, we get:
0 = 112 + 2(-3)s
0 = 121 - 6s
6s = 121
s = 121/6
s = 20.17 meters
Thus, the cyclist will travel approximately 20.17 meters before coming to a complete stop.
Classify the following expression by degree and term: (2 points)
x2y − 7xy + xyz + x
Answers
xyz - 5xy + x
Remember to always arrange terms in your polynomial in descending order according to the degree.
Now for degree, just get the sum of the exponents to determine the highest degree. The first term in the new equation has 3 variables, x,y, and z. Each of them, even when the power is not expressed are each raised to the power of 1. There are three variables so it will be:
1+1+1 = 3
The first term is classified as 3rd degree, which is the highest. So now you can conclude that this expression is a 3rd degree trinomial.
The given expression is a third-degree polynomial and consists of four terms: x^2y, -7xy, xyz, and x. Each term has a degree based on the sum of the exponents of the variables within it.
The expression in question is x2y − 7xy + xyz + x. To classify this expression by degree and by term, we need to look at the exponents of the variables in each term. The term 'degree' of a term in a polynomial is the sum of the exponents of the variables in that term.
x2y: The degree is 3 (2 from x2 and 1 from y).−7xy: The degree is 2 (1 from x and 1 from y).xyz: The degree is also 3 (1 from x, 1 from y, and 1 from z).x: The degree is 1, as there is only one occurrence of x.So the expression is a polynomial of third degree with four terms.
Luiza delivers newspapers in her neighborhood. If you plot the points (−1, 1), (4, 1), (4, −2) and (−1, −2), you will create a representation of the route she takes, in miles. How many miles does her route cover?
Answers
We have then that the resulting figure is a rectangle.
We must find the perimeter of the rectangle that is given by:
P = 2L + 2W
Where,
L: long
W: width
Restoring the values:
P = 2 * (5) + 2 * (3)
P = 16
Answer:
her route cover 16 miles.
Answer: 16 i just did this
Step-by-step explanation:
Find the area of the following ellipse Use = 3.14 and round to nearest tenth. a = 7 in.; b = 9 in.
Answers
Round to the nearest tenth
197.82~ 197.2 in^2
Answer:
197.82
Step-by-step explanation:
Suppose a triangle has two sides of the length 2and 3 and that the angle between these two sides is 60 what is the length of the third side of the triangle
Answers
.. c^2 = a^2 +b^2 -2ab*cos(C)
.. c^2 = 2^2 +3^2 -2*2*3*cos(60°)
.. c^2 = 7
.. c = √7 ≈ 2.6458
The third side of the triangle is √7, about 2.6458.
Answer: √7
Step-by-step explanation:
took the test
Which of the following is a solution of y - x > -3?
(6, 2)
(2, 6)
(2, -1)
Answers
y - x > -3
(6, 2) → x = 6, y = 2
substitute
2 - 6 = - 4 < -3 NOT
(2, 6) → x = 2, y = 6
substitute
6 - 2 = 4 > -3 CORRECT
(2, -1) → x = 2, y = -1
substitute
-1 - 2 = -3 NOT
Answer: (2, 6)
Assume that triangle GHI is congruent to LMN. Which of the following congruence statement are correct? check all that apply
Answers
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is a) ∠M= ∠H, c) ∠L=∠G. and e)IH=NM.
The congruence statements that are correct for the given scenario are △GHI ≅ △LMN, △IHG ≅ △NML, and △GIH ≅ △NML.
Explanation:The correct congruence statements for the given scenario are:
△GHI ≅ △LMN (by definition of congruence)△IHG ≅ △NML (by symmetry of congruence)△GIH ≅ △NML (by transitive property of congruence)These congruence statements indicate that the corresponding sides and angles of the triangles are equal, leading to overall congruence.
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The diameter of the base of a cylindrical can is 4 in. The height of the can is 6.5 in. Find the can’s surface area to the nearest tenth.
Answers
diameter of the base of a cylindrical can= 4 in----------> r=2 in
h=6.5 in
[surface area]=2*[pi*r²]+[2*pi*r*h]
then
[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²
the answer is 106.8 in²
Answer:
106.8 in2
Step-by-step explanation:
simplfy 5(9)
will give brainlest
Answers
Hope this helps!
For the following figure, complete the statement about the points. If U lies on the same line as R and N, what terms describe the relationship the three points must have?
Answers
Collinear because any points that is "on" the same line is considered collinear.
It can be Coplanar when any 3 points lie in the same plane, but this problem does not say that. It only asks if point U can be anywhere on the line including R and N.
Hope this helps! :) thanks to: Chaya1Cc for the most brainliest answer
The term that describes the relationship the three points must have is known as: collinear.
What are collinear points?Collinear points are points positioned on a shared straight line, forming a linear arrangement.
In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.
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A speech pathologist had a gross income of 62,650 last year. if 18.9% of her income got withheld for federal income tax how much of the pay got withheld for federal income tax last year
Answers
Answer:
$11,840.85
Step-by-step explanation:
hhhhhhhellllllllp.....................................
Answers
28/3 = 9.3333
The pen will be 9.3333 by 9.3333 meters
helpppppppppppppppppppppppppppppppppppppppp
Answers
What we must do in this case is to use the properties of the exponents:
We have then:
((x ^ (1/4)) * (y ^ 16)) ^ (1/2)
((x ^ (1/8)) * (y ^ 8))
answer:
((x ^ (1/8)) * (y ^ 8))
option number 2
evaluate -x+4y when -x=-4/5 and y= 1/3 write your anwser as a fraction or mixed number
Answers
= -4/5 + 4(1/3)
= -4/5 + 4/3
= -12/15 + 20/15
= 8/15
answer
8/15
The value of expression with the given x and y value is 8/15.
The given expression is -x+4y, -x=-4/5 and y=1/3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, put x=4/5 and y=1/3 in the given expression and simplify
That is, -4/5 + 4(1/3)
=-4/5 + 4/3
Take LCM of denominators 5 and 3 is 15
Now, -12/15 + 20/15
=(-12+20)/15
=8/15
Therefore, the value of expression with the given x and y value is 8/15.
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What is the rate of change and initial value for the linear relation that includes the points shown in the table?
x y
2 3
4 5
6 7
8 9
A. Initial value: 1, rate of change: 2 (Not the answer)
B. Initial value: 1, rate of change: 1
C. Initial value: 2, rate of change: 2 (Not the answer)
D. Initial value: 3, rate of change: 2
Answers
B. Initial value: 1, rate of change: 1
D is completely off. To get the initial value on a table you have to find the place where the input is zero.
So, you would take (2,3) and decrease both slots by 2 until x reaches zero. Now, we have (0,1). 1 is now our Initial Value.
To find the rate of change, you simply see how much the values increase/decrease. For example, let's take (6,7) and (8,9). As I said before, the input and output value increase by 2. Now, you put the change in 'y' over the change in 'x' and you have 2/2. After simplification, you are left with 1 as a whole number.
-Hope that wasn't too confusing, lol. I got a hundred on my test so I can assure you B. is correct. Good luck on your quiz :)
Answer:
Initial value: 1, rate of change: 1
Step-by-step explanation:
Took the FLVS test
.help me solve please and thank you✨
Answers
Kirstie is testing values that would make triangle klm a right triangle when ln is an altitude, and km = 16, as shown below. which lengths would make triangle klm a right triangle? 1) lm = 13 and kn = 6 2) lm = 12 and nm = 9 3) kl = 11 and kn = 7 4) ln = 8 and nm = 10
Answers
Answer: Option (2) is correct.
Step-by-step explanation:
Since we have given that
KLM is a right triangle, in which KM = 15, and ln is an altitude.
As we know that for right angled triangle, there are 3 conditions :
[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]
So, According to the options ,
Put LM = 12, NM = 9,
[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]
Since, it satisfies that KLM is a right triangle.
Hence, Option (2) is correct.
Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].
[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].
We will check each given option to see if the Pythagorean theorem holds.
Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:
[tex]\[ x = 16 - 6 = 10 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]
[tex]\[ 169 = LN^2 + 100 \][/tex]
[tex]\[ LN^2 = 69 \][/tex]
[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 69 \][/tex]
[tex]\[ KL^2 = 36 + 69 \][/tex]
[tex]\[ KL^2 = 105 \][/tex]
[tex]\[ KL \approx 10.2 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 9 = 7 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]
[tex]\[ 144 = LN^2 + 81 \][/tex]
[tex]\[ LN^2 = 63 \][/tex]
[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]
For [tex]\( \triangle KNL \):[/tex]
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 7^2 + 63 \][/tex]
[tex]\[ KL^2 = 49 + 63 \][/tex]
[tex]\[ KL^2 = 112 \][/tex]
[tex]\[ KL \approx 10.6 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:
[tex]\[ x = 16 - 7 = 9 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]
[tex]\[ 121 = 49 + LN^2 \][/tex]
[tex]\[ LN^2 = 72 \][/tex]
[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 72 + 9^2 \][/tex]
[tex]\[ LM^2 = 72 + 81 \][/tex]
[tex]\[ LM^2 = 153 \][/tex]
[tex]\[ LM \approx 12.4 \][/tex]
These calculations do not match the given [tex]\(LM\)[/tex] value.
Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 10 = 6 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]
[tex]\[ LM^2 = 64 + 100 \][/tex]
[tex]\[ LM^2 = 164 \][/tex]
[tex]\[ LM \approx 12.8 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]
[tex]\[ KL^2 = 36 + 64 \][/tex]
[tex]\[ KL^2 = 100 \][/tex]
[tex]\[ KL = 10 \][/tex]
These calculations match the given lengths.
Thus, the correct answer is:
D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]
The correct question is given below:
A student earned grades of C, A, B, and A in four different courses. Those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
To compute the GPA, multiply each grade by its corresponding credit hours, sum up the grade points, and divide by the total number of credit hours. In this case, the GPA is 3.40.
Explanation:To compute the grade point average (GPA), we need to multiply each grade by its corresponding number of credit hours to get the grade points. Then, we sum up the grade points and divide by the total number of credit hours. Here are the calculations:
Course 1: C grade (2 grade points) x 4 credit hours = 8 grade pointsCourse 2: A grade (4 grade points) x 5 credit hours = 20 grade pointsCourse 3: B grade (3 grade points) x 1 credit hour = 3 grade pointsCourse 4: A grade (4 grade points) x 5 credit hours = 20 grade pointsTotal grade points = 8 + 20 + 3 + 20 = 51 grade points
Total credit hours = 4 + 5 + 1 + 5 = 15 credit hours
GPA = Total grade points / Total credit hours = 51 / 15 = 3.40
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helpppppppppppppppppppppppppp
Answers
The fourth function is just a constant (with exponent 0), so it is an even function.
1. f(x) = (x-1)^2 = x^2 - 2x + 1
f(-x) = (-x-1)^2 = x^2 + 2x + 1
These two don't match, not an even function
2. f(x) = 8x
f(-x) = -8x
These two don't match, not an even function
3. f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
These two don't match, not an even function
4. f(x) = 7
f(-x) = 7
Match, is an even function
Why is circle 1 similar to circle 2?
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
.
A) Circle 1 is a dilation of circle 2 with a scale factor of 2.
.
B) Circle 1 is a dilation of circle 2 with a scale factor of 7.
.
C) Circle 1 is a translation of circle 2.
.
D) Circle 1 and circle 2 have the same center.
Answers
1/2 = r1/r2 = 14/7 = 2 --> dilation scale factor
We have a golden rule about similarity of figures. It is "All circle are always similar to each other".
In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.
The ratio of radii of two circles is called the scale factor of dilation between them.
Given are two circles with following information :-
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
Finding the ratio of their radii :-
[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]
So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.
Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.
The length of a rectangle is three more than twice the width. determine the dimensions that will give a total area of 27m^2
Answers
.. A = W*L
.. 27 = x*(3 +2x)
.. 2x^2 +3x -27 = 0
.. (2x +9)(x -3) = 0
.. x = {-4.5, 3} . . . . . . . . . . width, only the positive answer is of interest
.. 3 +2x = 3 +2*3 = 9 . . . . .this is the length
The rectangle is 3 m by 9 m.
What is the midpoint of the segment whose endpoints are (-6,5) and (4,-7)?
Answers
(-6+4)/2=x
(-2)/2=x
-1=x
(5+-7)/2=y
(-2)/2=y
-1=y
To start, the formula to find the midpoint coordinate pair of two given coordinates is as follows:
([tex] \frac{x1+x2}{2} [/tex], [tex] \frac{y1+y2}{2} [/tex])
Knowing this, plug in your given values (the two x values are -6 and 4; the two y values are 5 and -7) and simplify:
([tex] \frac{-6+4}{2} [/tex], [tex] \frac{5+-7}{2} [/tex])
=([tex] \frac{-2}{2} [/tex], [tex] \frac{-2}{2} [/tex])
=(-1,-1)
Therefore, the midpoint of the coordinates (-6,5) and (4,-7) would be (-1,-1).
Hope this helps and have a marvelous day! :)
What is a Banknote? Does a banknote have to come from the government?