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11. [-/1 Points] DETAILS LARPRECALCRMRP7 5.5.100.

Use the figure and trigonometric identities to find the exact value of the trigonometric function below in two ways.
4 cos(a) sin(3)
4 cos(a) sin(B) =
4 cos(a) sin(B) = 4? V (π/2-a)? V (π/2-B) =
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11. [-/1 Points] DETAILS LARPRECALCRMRP7 5.5.100. Use the figure and trigonometric-example-1
User GtEx
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Answer:

To find the exact value of the trigonometric function 4cos(a)sin(B) in two ways, we can use trigonometric identities and the given figure.

First way:

We know that the trigonometric identity for the product of cosine and sine is:

cos(a)sin(B) = (1/2)[sin(a + B) - sin(a - B)]

Using this identity, we can rewrite the expression:

4cos(a)sin(B) = 4[(1/2)[sin(a + B) - sin(a - B)]]

Simplifying further:

4cos(a)sin(B) = 2[sin(a + B) - sin(a - B)]

Second way:

In the given figure, we can see that angle a and angle B are complementary angles. This means that their sum is equal to 90 degrees or π/2 radians.

Using this information, we can rewrite the expression using trigonometric identities:

4cos(a)sin(B) = 4cos(a)cos(π/2 - B)

We can also use the identity for the product of cosine and cosine:

cos(a)cos(π/2 - B) = (1/2)[cos(a + (π/2 - B)) + cos(a - (π/2 - B))]

Simplifying further:

4cos(a)sin(B) = 2[cos(a + (π/2 - B)) + cos(a - (π/2 - B))]

In both ways, we have found the exact value of the trigonometric function 4cos(a)sin(B) using trigonometric identities and the given figure.

User Ymnk
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