Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine.
sin^6(x)
Answer=__________
~Thank you.
I believe this is the form I need to use..
sin^2(x)=(1-cos 2x)/(2)
I think I need to expand the problem with that, but I'm bit confused how..
To rewrite the expression sin^6(x) in terms of the first power of cosine, we can use the formula for the lowering power of sin:
sin^2(x) = 1 - cos^2(x)
We can rewrite sin^6(x) as (sin^2(x))^3.
Using the formula mentioned earlier, we substitute sin^2(x) with 1 - cos^2(x):
(sin^2(x))^3 = (1 - cos^2(x))^3
Expanding the expression using the binomial formula, we get:
(1 - cos^2(x))^3 = 1 - 3cos^2(x) + 3cos^4(x) - cos^6(x)
Now, notice that cos^2(x) represents the first power of cosine.
Therefore, the expression sin^6(x) in terms of the first power of cosine is:
1 - 3cos^2(x) + 3cos^4(x) - cos^6(x)
This is the final answer.