#### Inverse Trigonometric Functions Book Back Questions

12th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. The value of sin-1 (cos x),0$\le x\le\pi$ is

(a)

$\pi-x$

(b)

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

(c)

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

(d)

$\pi-x$

2. If cot−1x=$\frac{2\pi}{5}$ for some x$\in$R, the value of tan-1 x is

(a)

$\frac{-\pi}{10}$

(b)

$\frac{\pi}{5}$

(c)

$\frac{\pi}{10}$

(d)

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

3. The domain of the function defined by f(x)=sin−1$\sqrt{x-1}$ is

(a)

[1,2]

(b)

[-1,1]

(c)

[0,1]

(d)

[-1,0]

4. ${ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right)$is equal to

(a)

$\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(b)

$\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(c)

$\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right)$

(d)

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

5. If the function f(x)sin-1(x2-3), then x belongs to

(a)

[-1,1]

(b)

[$\sqrt2$,2]

(c)

$\\ \\ \\ \left[ -2,-\sqrt { 2 } \right] \cup \left[ \sqrt { 2 } ,2 \right]$

(d)

$\left[ -2,-\sqrt { 2 } \right] \cap \left[ \sqrt { 2 } ,2 \right]$

6. 3 x 2 = 6
7. Find the period and amplitude of
y=sin 7x

8. Find the principal value of
sec-1$(\frac{2}{\sqrt3})$

9. Find the value, if it exists. If not, give the reason for non-existence.
sin-1(cos$\pi$)

10. 3 x 3 = 9
11. For what value of x , the inequality$\cfrac { \pi }{ 2 } <{ cos }^{ -1 }(3x-1)<\pi$

12. Solve sin-1 x> cos-1x

13. Find the value of
$cos\left( { sin }^{ -1 }\left( \frac { 4 }{ 5 } \right) -{ tan }^{ -1 }\left( \frac { 3 }{ 4 } \right) \right)$

14. 2 x 5 = 10
15. Find the principal value of cos−1$\left( \frac { \sqrt { 3 } }{ 3 } \right)$

16. Find the principal value of
sec−1(−2).