Free Printable principal value branch of inverse trigonometric functions

1.

Principal branch of $\tan^{-1}x$ is __________.

a)

$\left(\frac{-\pi}{2},\frac{\pi}{2}\right)$

b)

$\left[\frac{-\pi}{2},\frac{\pi}{2}\right]$

c)

$\left[0,\pi\right]$

d)

$\left(0,\pi\right)$

2.

Principal value branch of $\sec^{-1}\left(-2\right)$

a)

$\frac{-2\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$\frac{2\pi}{3}$

d)

$\frac{-\pi}{3}$

3.

$Find\ the\ value\ of\ \tan^{-1}\left[2\cos\left(2\sin^{-1}\left(\frac{1}{2}\right)\right)\right]$

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{2}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{4}$

4.

$Find\ the\ value\ of\cos^{-1}\left(\frac{1}{2}\right)-2\sin^{-1}\left(-\frac{1}{2}\right).$

a)

$\frac{\pi}{3}$

b)

$\frac{2\pi}{3}$

c)

$-\frac{2\pi}{3}$

d)

$\pi$

5.

$Find\ the\ value\ of\ \cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)$

a)

$\frac{5\pi}{6}$

b)

$-\frac{\pi}{6}$

c)

$-\frac{5\pi}{6}$

d)

$\frac{\pi}{6}$

6.

$Write\ the\ principal\ vale\ of\ \tan^{-1}\left(-\sqrt{3}\right).$

a)

$\frac{\pi}{3}$

b)

$-\frac{\pi}{6}$

c)

$-\frac{\pi}{3}$

d)

$\frac{\pi}{6}$

7.

$evaluate\ \tan^{-1}\left\{\sin\left(-\frac{\pi}{2}\right)\right\}$

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$-\frac{3\pi}{4}$

d)

$-\frac{\pi}{4}$

8.

$The\ value\ of\ \cos^{-1}\left(\frac{1}{2}\right)+3\sin^{-1}\left(\frac{1}{2}\right)\ is\ eual\ to$ The value of

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{6}$

c)

$\frac{2\pi}{3}$

d)

$\frac{5\pi}{6}$

9.

$Find\ the\ value\ of\ \tan^{-1}\left(1\right)+\cos^{-1}\left(-\frac{1}{2}\right)+\sin^{-1}\left(-\frac{1}{2}\right)$

a)

$-\frac{3\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$\frac{5\pi}{6}$

d)

$-\frac{5\pi}{6}$

10.

$Domain\ of\ \sec^{-1}x\ is$

a)

$R$

b)

$R-\left\{0\right\}$

c)

$\left[-1,1\right]$

d)

$R-\left(-1,1\right)$

principal value branch of inverse trigonometric functions

Total questions: 10

Worksheet time: 10mins

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