Trigonometric identies(shifting by pi/2)

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Last updated 4:50 AM on 4/18/26
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6 Terms

1
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What is the sine of an angle shifted by π2\frac{\pi}{2}?

sin⁡(x+π2)=cos⁡(x)\sin\left(x + \frac{\pi}{2}\right) = \cos(x).

2
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What is the cosine of an angle shifted by π2\frac{\pi}{2}?

cos⁡(x+π2)=−sin⁡(x)\cos\left(x + \frac{\pi}{2}\right) = -\sin(x).

3
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What is the tangent of an angle shifted by π2\frac{\pi}{2}?

tan⁡(x+π2)=−cot⁡(x)\tan\left(x + \frac{\pi}{2}\right) = -\cot(x).

4
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What is the cosecant of an angle shifted by π2\frac{\pi}{2}?

csc⁡(x+π2)=−sec⁡(x)\csc\left(x + \frac{\pi}{2}\right) = -\sec(x).

5
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What is the secant of an angle shifted by π2\frac{\pi}{2}?

sec⁡(x+π2)=−csc⁡(x)\sec\left(x + \frac{\pi}{2}\right) = -\csc(x).

6
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What is the cotangent of an angle shifted by π2\frac{\pi}{2}?

cot⁡(x+π2)=−tan⁡(x)\cot\left(x + \frac{\pi}{2}\right) = -\tan(x).