Simplify sin(-pi)+cos(5pi)

Problem

sin(−π)+cos(5*π)

Solution

1. Evaluate the sine term using the property of the unit circle or the fact that sine is an odd function, sin(−θ)=−sin(θ)

sin(−π)=−sin(π)

sin(π)=0

sin(−π)=0

2. Evaluate the cosine term by using the periodicity of the cosine function, cos(θ+2*k*π)=cos(θ) for any integer k

cos(5*π)=cos(π+4*π)

cos(5*π)=cos(π)

cos(π)=−1

3. Substitute the values back into the original expression and perform the addition.

0+(−1)=−1

Final Answer

sin(−π)+cos(5*π)=−1

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