Question

How to find a value of t within [0,2π] that satisfies cos(t) = sin(2t)?

A) t = π/2
B) t = π/3
C) t = 3π/4
D) t = 2π/3

Answer 1

To find a value of t within [0,2π] that satisfies cos(t) = sin(2t), use the trigonometric identity sin(2t) = 2sin(t)cos(t). Divide both sides by cos(t) to get sin(t) = 1/2. The correct values of t are t = π/6 and t = 5π/6.

Step-by-step explanation:

To find a value of t within [0,2π] that satisfies cos(t) = sin(2t), we can use the trigonometric identity: sin(2t) = 2sin(t)cos(t). Plugging this into the equation, we get cos(t) = 2sin(t)cos(t). Since cos(t) is not equal to zero for any value of t within [0,2π], we can divide both sides by cos(t) to get 1 = 2sin(t). Dividing by 2, we get sin(t) = 1/2. This occurs at t = π/6 and t = 5π/6 within the given range [0,2π]. Therefore, the correct values of t are t = π/6 and t = 5π/6, which are not options A, B, C, or D.