Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of sine and cosine.sin3(x)
Question
Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of sine and cosine.sin3(x)
Solution
The power-reducing identities are:
sin²(x) = 1/2 - 1/2 cos(2x) cos²(x) = 1/2 + 1/2 cos(2x)
However, your expression is sin³(x), not sin²(x). To rewrite sin³(x) in terms of first powers of sine and cosine, we can use the identity sin³(x) = (3sin(x) - sin(3x))/4.
So, sin³(x) can be rewritten as (3sin(x) - sin(3x))/4.
Similar Questions
Use the sum-to-product identities to rewrite the following expression in terms containing only first powers of tangent. sin8x−sin2xcos8x+cos2x
Use the product-to-sum identities to rewrite the following expression as a sum or difference.4sin(3x)sin(x)
When proving identities, it is sometimes helpful to convert everything to sines and cosines first.Group of answer choicesTrueFalse PreviousNext
Simplify the expression.tan(sin−1(x))
Simplify the expression.sin2x + sinx + cos 2x - 1
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.