Answer:
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Step-by-step explanation:
Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
The length of an arc is given by θ/360×2πr, where θ is angle subtended by the arc to the center and r is the radius of the circle.
The length is 12 units, and θ/360 is 1/3
Therefore, 12 = 1/3 × 3.142 ×r
r = 12× 3/3.142
r = 11.457 units
≈ 11 units