Trigonometric Ratios of Standard Angles Quiz - ICSE Class 9 Mathematics

Free practice quiz: Trigonometric Ratios of Standard Angles (ICSE Class 9 Mathematics). 45 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 9 Mathematics practice quiz has 45 multiple-choice questions on Trigonometric Ratios of Standard Angles, and 45 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If $\sin \theta = \frac{\sqrt{3}}{2}$ and $\theta$ is an acute angle, then find the value of $2\cos \theta$.

   1. 1
   2. 2
   3. $\frac{1}{2}$
   4. $\sqrt{3}$
   Show answer

   Answer: A. 1

   Given $\sin \theta = \frac{\sqrt{3}}{2}$, for an acute angle $\theta$, we know that $\theta = 60^\circ$. Then, $\cos \theta = \cos 60^\circ = \frac{1}{2}$. Therefore, $2\cos \theta = 2 \times \frac{1}{2} = 1$.

2. Calculate: $\cos^2 0^\circ + \sin^2 90^\circ + 2 \tan 45^\circ$.

   1. 2
   2. 3
   3. 4
   4. 5
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   Answer: C. 4

   We know that $\cos 0^\circ = 1$, $\sin 90^\circ = 1$, and $\tan 45^\circ = 1$. So, $\cos^2 0^\circ = 1^2 = 1$, $\sin^2 90^\circ = 1^2 = 1$. The expression becomes $1 + 1 + 2(1) = 1 + 1 + 2 = 4$.

3. If $\sin x = \frac{\sqrt{3}}{2}$ and $\cos x = \frac{1}{2}$, what is $\tan x$?

   1. $\frac{1}{\sqrt{3}}$
   2. 1
   3. $\sqrt{3}$
   4. 2
   Show answer

   Answer: C. $\sqrt{3}$

   We know that $\tan x = \frac{\sin x}{\cos x}$. Given $\sin x = \frac{\sqrt{3}}{2}$ and $\cos x = \frac{1}{2}$, $\tan x = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \frac{\sqrt{3}}{2} \times \frac{2}{1} = \sqrt{3}$.

4. Calculate: $\sin^2 45^\circ + \cos^2 45^\circ + \tan^2 45^\circ$.

   1. 1
   2. 2
   3. 3
   4. 4
   Show answer

   Answer: B. 2

   Using the identity $\sin^2 \theta + \cos^2 \theta = 1$, we have $\sin^2 45^\circ + \cos^2 45^\circ = 1$. We also know that $\tan 45^\circ = 1$, so $\tan^2 45^\circ = 1^2 = 1$. Therefore, the expression is $1 + 1 = 2$.

5. If $\tan heta = \frac{1}{\sqrt{3}}$ and $ heta$ is acute, find $\cos heta$.

   1. 1
   2. $\frac{1}{2}$
   3. $\frac{\sqrt{3}}{2}$
   4. $\frac{1}{\sqrt{2}}$
   Show answer

   Answer: C. $\frac{\sqrt{3}}{2}$

   If $ an heta = \frac{1}{\sqrt{3}}$ and $ heta$ is acute, then $ heta = 30^\circ$. Therefore, $\cos heta = \cos 30^\circ = \frac{\sqrt{3}}{2}$.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the value of $\tan 30^\circ + \cot 60^\circ$?
2. If $\cos \alpha = \frac{1}{2}$ and $\alpha$ is an acute angle, find the value of $\sin \alpha$ multiplied by $\tan \alpha$.
3. If $\theta = 45^\circ$, find the value of $\frac{\sin \theta + \cos \theta}{1 + \tan \theta}$.
4. Find the value of $\frac{\tan 60^\circ + \sin 90^\circ}{\cos 0^\circ - \tan 45^\circ}$.
5. If $\sin x = \frac{1}{2}$ and $x$ is an acute angle, what is the value of $\cos x + \tan x$?
6. If $\theta$ is an acute angle such that $\cos \theta = \frac{\sqrt{3}}{2}$, what is the value of $\sin \theta$?
7. Find the value of $\frac{\tan 60^\circ}{\sin 60^\circ}$.
8. If $\sin \theta = \frac{1}{\sqrt{2}}$ and $\theta$ is an acute angle, what is $\tan \theta$?
9. If $\tan \theta = 1$ and $\theta$ is an acute angle, what is $\sin \theta + \cos \theta$?
10. Evaluate: $\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ$.
11. What is the value of $\frac{\sin 90^\circ + \tan 0^\circ}{\cos 0^\circ}$?
12. If $\sin \theta = \frac{1}{2}$ and $\theta$ is acute, find the value of $\sec \theta$.
13. Evaluate: $\frac{\sin 30^\circ + \tan 45^\circ}{\cos 0^\circ - \sin 90^\circ}$.
14. If $\cos \theta = \frac{1}{2}$ and $\theta$ is acute, what is $\tan \theta$?
15. If $\theta = 60^\circ$, what is the value of $\sin^2 \theta + \cos^2 \theta$?
16. Find the value of $\frac{2\tan 30^\circ}{1 + \tan^2 30^\circ}$.
17. If $\tan \theta = \sqrt{3}$ and $\theta$ is acute, find $\sin \theta$.
18. What is the value of $(\sin 45^\circ + \cos 45^\circ)^2$?
19. If $\theta = 30^\circ$, find $\frac{\sin \theta}{\cos \theta}$.
20. Evaluate: $2\sin 30^\circ + 2\cos 60^\circ$.
21. If $\sin \theta = 1$ and $\theta$ is an acute angle, find $\tan \theta$.
22. If $\theta = 30^\circ$, what is $\sin^2 \theta$?
23. Evaluate: $2 \times (\sin 60^\circ + \cos 30^\circ)$.
24. If $\sin \theta = \frac{1}{2}$ and $\theta$ is acute, find $\cot \theta$.
25. If $\cos \theta = \frac{1}{\sqrt{2}}$ and $\theta$ is acute, find $\sin \theta$.
26. Evaluate: $\frac{\tan 60^\circ \times \sin 30^\circ}{\cos 0^\circ}$.
27. If $\sin x = \frac{1}{2}$ and $x$ is acute, what is $\cos x$?
28. Calculate: $(\sin 30^\circ + \cos 60^\circ) \times \tan 45^\circ$.
29. If $\tan x = 1$ and $x$ is acute, find $\sin x$.
30. Evaluate: $\frac{\sin 90^\circ + \cos 0^\circ}{\tan 45^\circ}$.
31. If $\sin heta = \frac{1}{2}$ and $ heta$ is acute, find $\sec heta$.
32. Evaluate: $\sin 45^\circ \times \cos 45^\circ$.
33. What is the value of $\tan 45^\circ + \cot 45^\circ$?
34. Evaluate: $\frac{\sin 30^\circ}{\tan 45^\circ}$.
35. If $\tan heta = 1$ and $ heta$ is acute, what is $\cos heta$?
36. If $\theta = 30^\circ$, what is $\sin^2 \theta + \cos^2 \theta$?
37. Evaluate: $\tan 60^\circ \times \cot 60^\circ$.
38. If $\sin heta = \frac{\sqrt{3}}{2}$ and $ heta$ is acute, find $ an heta$.
39. Calculate: $\cos^2 45^\circ - \sin^2 45^\circ$.
40. If $\theta = 30^\circ$, find $\frac{\tan \theta}{\sin \theta}$.

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