Class 9 Trigonometrical Ratios of Standard Angles Mock Test (ICSE)

Topics in Trigonometrical Ratios of Standard Angles

• Ratios of 0, 30, 45, 60 and 90 degrees
• Evaluating expressions with standard angles
• Solving simple trigonometric equations

Trigonometrical Ratios of Standard Angles practice questions with answers

1. Q1Multiple choice·1 mark
   The value of $\tan^2 60^\circ - \sec^2 45^\circ$ is:

   1. (a)$0$
   2. (b)$2$
   3. (c)$3$
   4. (d)$1$
   Show answer and step marks

   1. Correct option: (d) $1$. Substitute standard values $\tan 60^\circ = \sqrt{3}$ and $\sec 45^\circ = \sqrt{2}$ to obtain $(\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1$, making option (d) correct.+1

   Answer: (d)
2. Q2Multiple choice·1 mark
   If $\sqrt{3} \tan x = 1$, where $x$ is an acute angle, then the value of $x$ is:

   1. (a)$30^\circ$
   2. (b)$60^\circ$
   3. (c)$15^\circ$
   4. (d)$45^\circ$
   Show answer and step marks

   1. Correct option: (a) $30^\circ$+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   What is the value of $\sin 0^\circ + \cos 0^\circ + \tan 45^\circ$?

   1. (a)$0$
   2. (b)$1$
   3. (c)$2$
   4. (d)$3$
   Show answer and step marks

   1. Correct option: (c) $2$+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   Evaluate $\frac{\sin 30^\circ}{\cos 60^\circ} \times \tan 45^\circ$.

   1. (a)$2$
   2. (b)$\frac{1}{2}$
   3. (c)$0$
   4. (d)$1$
   Show answer and step marks

   1. Correct option: (d) $1$+1

   Answer: (d)
5. Q5Short answer·2 marks
   Evaluate the following expression: $4(\sin^2 30^\circ + \cos^2 60^\circ) + 3(\tan^2 30^\circ \times \tan^2 60^\circ)$
   Show answer and step marks

   1. Substitute the standard values: $\sin 30^\circ = \frac{1}{2}$, $\cos 60^\circ = \frac{1}{2}$, $\tan 30^\circ = \frac{1}{\sqrt{3}}$, and $\tan 60^\circ = \sqrt{3}$.+1
   2. Simplify: $4\left(\left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2\right) + 3\left(\left(\frac{1}{\sqrt{3}}\right)^2 \times (\sqrt{3})^2\right) = 4\left(\frac{1}{4} + \frac{1}{4}\right) + 3\left(\frac{1}{3} \times 3\right) = 4\left(\frac{1}{2}\right) + 3(1) = 2 + 3 = 5$.+1

   Answer: $5$

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