Find the Exact Value sin(13pi)

Problem

sin(13*π)

Solution

1. Identify the periodicity of the sine function. The sine function has a period of 2*π which means sin(θ)=sin(θ+2*k*π) for any integer k

2. Rewrite the angle 13*π in terms of the period 2*π We can express 13*π as 12*π+π

3. Apply the periodicity rule. Since 12*π is a multiple of 2*π (where k=6, the value of sin(13*π) is equivalent to sin(π)

sin(13*π)=sin(12*π+π)

sin(13*π)=sin(π)

4. Evaluate the sine of π using the unit circle. At the angle π radians (or 180, the coordinates on the unit circle are (−1,0) Since sin(θ) corresponds to the y-coordinate, sin(π)=0

Final Answer

sin(13*π)=0

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