Find the value of ^-1 ( ((33π)/(5) ) ).

MathsCBSE Class 12 · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2023-24: question 21(a)

From the official CBSE sample question paper for 2023-24, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerInverse Trigonometric Functions

Find the value of $sin^{- 1} (cos (\frac{33 π}{5}))$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

Remove multiples of $2 π$ from $\frac{33 π}{5}$ first.

Hint 2

Write $cos θ$ as $sin (\frac{π}{2} - θ)$ and check that the angle lies in $[- \frac{π}{2}, \frac{π}{2}]$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Since $cos$ has period $2 π$ : $cos \frac{33 π}{5} = cos (6 π + \frac{3 π}{5}) = cos \frac{3 π}{5} = sin (\frac{π}{2} - \frac{3 π}{5}) = sin (- \frac{π}{10})$ .
1 mark
$- \frac{π}{10} \in [- \frac{π}{2}, \frac{π}{2}]$ , the principal value branch of $sin^{- 1}$ . So $sin^{- 1} (cos \frac{33 π}{5}) = sin^{- 1} (sin (- \frac{π}{10})) = - \frac{π}{10}$ .
1 mark

Answer: $- \frac{π}{10}$

Where the marks are

Reduces $cos \frac{33 π}{5}$ to $sin (\frac{π}{2} - \frac{3 π}{5})$ (1 mark)
Uses the principal branch to get $- \frac{π}{10}$ (1 mark)

Revise the chapter

Chapter: Inverse Trigonometric Functions (notes, formulas, where marks are lost and every past question)
Topic: Principal Values of Inverse Trigonometric Functions

Practise this chapterBoard-style questions from Inverse Trigonometric Functions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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