12th
grade

Mathematics

50%

accuracy

205

plays

SANJEEV KUMAR

4 years

Mathematics

12th

grade

inverse Trigonometric Functions

SANJEEV KUMAR

205
plays

21 questions

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1. Multiple Choice
2 minutes
1 pt
What test will you use to determine if a function is one-to-one?
Veetical Line Test
Horizontal Line Test
One-to-one Test
Function Domain-Range Test
2. Multiple Choice
2 minutes
1 pt
Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$-\frac{\pi}{3}$
$\frac{\pi}{3}$
$-\frac{\pi}{6}$
$\frac{\pi}{6}$
3. Multiple Choice
2 minutes
1 pt
Find the exact value of $\sec^{-1}\left(-2\right)$
$\frac{2\pi}{3}$
$-\frac{\pi}{3}$
$\frac{4\pi}{3}$
$-\frac{2\pi}{3}$
4. Multiple Choice
2 minutes
1 pt
What is the restricted domain of the cosine function in order to have an inverse cosine function?
$\left[0,\pi\right]\ -\ \left\{\frac{\pi}{2}\right\}$
$\left[0,\pi\right]$
$\left[-1,1\right]$
$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
5. Multiple Choice
2 minutes
1 pt
Inverse Functions
Not Inverse Functions
6. Multiple Choice
2 minutes
1 pt
What operation allows us to verify if functions are inverses?
Multiplying
Dividing
Adding
Composing
7. Multiple Choice
2 minutes
1 pt
$\tan\left(\sin^{-1}\left(\frac{5}{13}\right)\right)$ is
5/12
5/13
3/13
3/5
8. Multiple Choice
2 minutes
1 pt
$\cos\left(\sin^{-1}\frac{\text{1}}{\text{4}}+\sec^{-1}\frac{4}{3}\right)$

$\frac{\left(3\sqrt{15}-\sqrt{7}\right)}{16}$
$\frac{\left(3\sqrt{15}-\sqrt{7}\right)}{4}$
$\frac{\left(3\sqrt{15}+\sqrt{7}\right)}{16}$
$\frac{\left(3\sqrt{15}+\sqrt{7}\right)}{4}$
9. Multiple Choice
2 minutes
1 pt
Range of function $\tan^{-1}x\ is$
R
$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
$R-\left\{\frac{\pi}{2}\right\}$
$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$
10. Multiple Choice
2 minutes
1 pt
$\cot^{-1}\left[\cot\left(\frac{-9\pi}{4}\right)\right]$
$\frac{\pi}{4}$
$\frac{-\pi}{4}$
$\frac{-3\pi}{4}$
$\frac{3\pi}{4}$
11. Multiple Choice
2 minutes
1 pt
If xy<1, then $\tan^{-1}x+\tan^{-1}y=------$
$\tan^{-1}\left(\frac{x-y}{1+xy}\right)$
$\tan^{-1}\left(\frac{x+y}{1-xy}\right)$
$\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)$
$\pi-\tan^{-1}\left(\frac{x+y}{1-xy}\right)$
12. Multiple Choice
2 minutes
1 pt
$The\ value\ of\ \sin^{-1}x+\cos^{-1}x,\ \ \ \ \ x∈[-1,1]$
$=1$
$=\frac{\pi}{2}$
$=\pi$
$=0$
13. Multiple Choice
2 minutes
1 pt
$\tan^{-1}x+\cot^{-1}x=π/2\ when$
$x∈\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$
$x\in R$
$x\in+R$
$x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$
14. Multiple Choice
2 minutes
1 pt
$\tan^2(\sec^{-1}2)+\cot^2(\operatorname{cosec}^{-1}3)\ =$
3
11
13
15
15. Multiple Choice
2 minutes
1 pt
sin[cot^-1(-5)]
(5√26)/26
-(5√26)/26
-(√26)/26
(√26)/26
16. Multiple Choice
2 minutes
1 pt
$\tan^{-1}(m/n)-\tan^{-1}[(m-n)/(m+n)]$
π/3
π/4
π/2
-3π/4
17. Multiple Choice
2 minutes
1 pt
Identify the domain of $f\left(x\right)=\cos^{-1}\left(2x\right)$
$-2\le x\le2$
$-\frac{1}{2}\le x\le\frac{1}{2}$
$-1\le x\le1$ $-1<x<1$
$-\infty<x<\infty$
18. Multiple Choice
30 seconds
1 pt
tan(cos^-1(-1))=
undefined
0
½
1
19. Multiple Choice
30 seconds
1 pt
1. The value of
$\cos^{-1\ }\left(\cos\ \frac{7\pi}{6}\right)$ is
$\frac{\pi}{6}$
$-\frac{\pi}{6}$
$\frac{7\pi}{6}$
$\frac{5\pi}{6}$
20. Multiple Choice
30 seconds
1 pt
$\sin\ \left(\frac{\pi}{3}\ -\ \sin^{-1}\left(-\frac{1}{2}\right)\right)\ =$
1
- 1
0
$\frac{1}{2}$
21. Multiple Choice
30 seconds
1 pt

$\sin\left(\sin^{-1\ }\left(x\right)\right)\ =\ x\ only\ if$
$\left|x\right|\le1$
$\left|x\right|\ge1$
$-\frac{\pi}{2}\le x\le\frac{\pi}{2}$
$0\le x\le\pi$
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