Answer:
(1/2)(sin(105°) +sin(345°))
Step-by-step explanation:
The relevant identity is ...
sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))
This falls out directly from the sum and difference formulas for sine.
Here, you have α = 45° and β = 60°, so the relevant expression is ...
sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))
Recognizing that -15° has the same trig function values that 345° has, this can be written ...
sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))
Given that angle A is 45 degrees and angle B is 60 degrees, we use the product-to-sum identity in Trigonometry to find sin(A)cos(B). The correct answer after simplifying the formula sin(A)cos(B) = ½ [sin(A + B) + sin(A - B)] is ½ [sin(105) + sin(345)].
Explanation:In Mathematics, especially Trigonometry, there is a formula known as product-to-sum identities. One of the identities is Sin(A)Cos(B) = ½ [sin(A + B) + sin(A - B)].
Given that angle A is 45 degrees and angle B is 60 degrees, we will find sin(A)cos(B) by substituting A and B in the formula.
On substitution you get ½ [sin(45 + 60) + sin(45 - 60)], which simplifies to ½ [sin(105) + sin(-15)]. Note that sin(-15) is equivalent to sin(345) in the unit circle, therefore the expression further simplifies to ½ [sin(105) + sin(345)].
Learn more about Product-to-Sum Identity here:https://brainly.com/question/34814515
#SPJ11
Please help with these partial sum questions??
a. If c is a constant then the sum of such constants is the same as multiplication of constants. Therefore [tex]\Sigma_{k=1}^{n}c=nc[/tex]
b. [tex]\Sigma_{k=1}^{n}k=1+2+3+\dots+\infty=\infty[/tex]
c. [tex]\Sigma_{k=1}^{n}k^2=1+4+9+\dots+\infty=\infty[/tex]
d. [tex]\Sigma_{k=1}^{n}k^3=1+8+27+\dots+\infty=\infty[/tex]
Hope this helps.
r3t40
HELP!
What is the solution set of |2x + 1| > 5?
A {x|1 < x < –3}
B {x|–1 < x < 3}
C {x|x > 2 or x < –3}
D {x|x < 2 or x > –3}
Answer:
Answer choice C
Step-by-step explanation:
When the values of x are greater than 2, the solution works. When the values oclf x are less than 3, the solution also works. :)
Answer:
C
Step-by-step explanation:
Inequalities of the form | x | > a have solutions of the form
x < - a OR x > a, thus
2x + 1 < - 5 OR 2x + 1 > 5 ( subtract 1 from both sides of both )
2x < - 6 OR 2x > 4 ( divide both sides of both by 2)
x < - 3 OR x > 2
Solution set is
{ x | x > 2 or x < - 3 } → C
find the perimeter of the triangle to the nearest unit with vertices A(-2,4) B(-2,-2) and C(4,-2)
Answer:
20
Step-by-step explanation:
Use the distance equation to find the length of each side:
d = √((x₂ − x₁)² + (y₂ − y₁)²)
where (x₁, y₁) and (x₂, y₂) are the points (the order doesn't matter).
AB:
d = √((-2 − (-2))² + (-2 − 4)²)
d = 6
BC:
d = √((4 − (-2))² + (-2 − (-2))²)
d = 6
AC:
d = √((-2 − 4)² + (4 − (-2))²)
d = 6√2
So the perimeter is:
AB + BC + AC
6 + 6 + 6√2
≈ 20