Given that θ = a/b, then θ is. (A) (b)/(√(b²-a²)) (B) b/a (C) (√(b²-a²))/(b) (D) (a)/(√(b²-a²))

MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 11

From the official CBSE sample question paper for 2023-24, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQIntroduction to Trigonometry

Given that $sin θ = \frac{a}{b}$ , then $cos θ$ is.

(A) $\frac{b}{b ^{2} - a ^{2}}$
(B) $\frac{b}{a}$
(C) $\frac{b ^{2} - a ^{2}}{b}$
(D) $\frac{a}{b ^{2} - a ^{2}}$

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

Draw a right triangle with $sin θ = a / b$ .

Hint 2

Use $cos θ$ = adjacent/hypotenuse.

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.

Take a right triangle with opposite side $a$ and hypotenuse $b$ . The adjacent side is $b^{2} - a^{2}$ (Pythagoras).
$cos θ = \frac{b ^{2} - a ^{2}}{b}$ . Option (C).
1 mark

Answer: $\frac{b ^{2} - a ^{2}}{b}$ , option (C)

Where the marks are

Finds the adjacent side by Pythagoras and gets $cos θ$ , option (C) (1 mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
Topic: Relationships Between Trigonometric Ratios

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

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 11

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry