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CBSE · Class 10 · Mathematics · Introduction to TrigonometryIf $\sin A = \frac{3}{4}$, then what is the value of $\cos A$?

Step-by-Step Solution

Using the trigonometric identity $\sin^2 A + \cos^2 A = 1$:

$$\cos^2 A = 1 - \sin^2 A$$ $$\cos^2 A = 1 - \left(\frac{3}{4}\right)^2 = 1 - \frac{9}{16} = \frac{16 - 9}{16} = \frac{7}{16}$$ \nTaking the square root on both sides: $$\cos A = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}$$ \nHence, the correct option is (B).

Detailed Options Breakdown
Option : $\frac{4}{3}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 1: $\frac{\sqrt{7}}{4}$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: $\frac{3}{\sqrt{7}}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 3: $\frac{\sqrt{7}}{3}$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

💡 Study Guide: This question tests core syllabus concepts from Introduction to Trigonometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Trigonometry Revision Notes.
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