Chapter 7: Q 3. (page 457)

If $\tan θ = \frac{1}{2}, - \frac{π}{2} < θ < \frac{π}{2}$ then $\sin θ =_______$ .

Short Answer

Expert verified

If $\tan θ = \frac{1}{2}, - \frac{π}{2} < θ < \frac{π}{2}$ then $S i n θ = \frac{\sqrt{5}}{5}$ .

Step by step solution

Step 1. Given information.

$\tan θ = \frac{1}{2}, - \frac{π}{2} < θ < \frac{π}{2}$

. Value ofTan θ.

Here, $θ$ lies between $- \frac{π}{2}$ and $\frac{π}{2}$ .But tan positive in first and third quadrants. So, $θ$ lies in first quadrant.

$\tan θ = \frac{o p p o s i t e}{a d j a c e n t}$

Step 3. Using Pythagorean theorem.

$H^{2} = P^{2} + B^{2} H^{2} = 1^{2} + 2^{2} H^{2} = 1 + 4 H = \sqrt{5}$

Step 4. Value of Sinθ.

$S i n θ = \frac{o p p o s i t e}{h y p o t e n u s e} S i n θ = \frac{1}{\sqrt{5}} S i n θ = \frac{1 \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} S i n θ = \frac{\sqrt{5}}{5}$

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If $\tan θ = \frac{1}{2}, - \frac{π}{2} < θ < \frac{π}{2}$ then $\sin θ =_______$ .

Short Answer

Step by step solution

Step 1. Given information.

. Value ofTan θ.

Step 3. Using Pythagorean theorem.

Step 4. Value of Sinθ.

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Iftanθ=12,-π2<θ<π2then sinθ=_______.

Short Answer

Step by step solution

Step 1. Given information.

. Value ofTan θ.

Step 3. Using Pythagorean theorem.

Step 4. Value of Sinθ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

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Pure Maths

Study anywhere. Anytime. Across all devices.

If $\tan θ = \frac{1}{2}, - \frac{π}{2} < θ < \frac{π}{2}$ then $\sin θ =_______$ .