Chapter 13: Q14. (page 706)

If $\tan (θ) = 3$ , find the value of $\sin (θ)$ .
localid="1648455893738" $(A) \frac{3}{10} (B) \frac{3 \sqrt{10}}{10} (C) \frac{10}{3} (D) \frac{1}{3}$

Short Answer

Expert verified

The value of $\sin (θ) = \frac{3 \sqrt{10}}{10}$ .Hence,option (B) is correct.

Step by step solution

Step 1. Write down the given information.

It is given that $\tan (θ) = 3$

Step 2. Calculation.

Since $\tan (θ) = 3$ , therefore construct the triangle ABC having angle $C = θ$ , base $B C = 1$ , perpendicular height $A B = 3$ and angle $B = 90 °$ .

Now, by Pythagoras Theorem,

$\begin{matrix} A C = \sqrt{A B^{2} + B C^{2}} \\ = \sqrt{3^{2} + 1^{2}} \\ = \sqrt{10} \end{matrix}$

Now in right triangle ABC by trigonometric ratios,

$\begin{matrix} \sin (C) = \frac{A B}{A C} \\ \sin (θ) = \frac{3}{\sqrt{10}} \\ \sin (θ) = \frac{3 \sqrt{10}}{10} \end{matrix}$

Since, the value of $\sin (θ) = \frac{3 \sqrt{10}}{10}$ . Hence, option (B) is correct.

Step 3. Conclusion.

The value of $\sin (θ) = \frac{3 \sqrt{10}}{10}$ . Hence, option (B) is correct.

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If $\tan (θ) = 3$ , find the value of $\sin (θ)$ .
localid="1648455893738" $(A) \frac{3}{10} (B) \frac{3 \sqrt{10}}{10} (C) \frac{10}{3} (D) \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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If tanθ=3, find the value of sinθ.localid="1648455893738" A310B31010C103D13

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Statistics

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

If $\tan (θ) = 3$ , find the value of $\sin (θ)$ .
localid="1648455893738" $(A) \frac{3}{10} (B) \frac{3 \sqrt{10}}{10} (C) \frac{10}{3} (D) \frac{1}{3}$