What is $sin (x + \frac{π}{2})$ $sin(x+pi/2)$ ?

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What is $sin (x + \frac{π}{2})$ $sin(x+pi/2)$ ?

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Answer 1 · 2015-04-16T04:24:37

cos x

With $\frac{π}{2}$ $pi/2$ add to any angle measure, sin changes to cos and vice- versa. Hence It would change to cosine and since the angle measure falls in the second quadrant, hence sin(x+ $\frac{π}{2}$ $pi/2$ ) would be positive.

Alternatively sin(x+ $\frac{π}{2}$ $pi/2$ )= sin x cos $\frac{π}{2}$ $pi/2$ + cos x sin $\frac{π}{2}$ $pi/2$ . Since cos $\frac{π}{2}$ $pi/2$ is 0 and sin $\frac{π}{2}$ $pi/2$ is 1, it would be equal to cosx

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What is $sin (x + \frac{π}{2})$ $sin(x+pi/2)$ ?

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