Chapter 7: Q. 19 (page 504)

Use the Half-angle Formulas to find the exact value of each expression.
$\sin 22.5 °$ .

Short Answer

Expert verified

The value of the expression $\sin 22.5 °$ is $\sqrt{\frac{2 - \sqrt{2}}{2}}$

Step by step solution

Step 1. Given information

The given expression is $\sin 22.5 °$

Step 2. Find the value.

We know that, $\sin 22.5 ° = \sin \frac{45 °}{2} \sin \frac{45 °}{2} = \sqrt{\frac{1 + \cos θ}{2}} \sin \frac{45 °}{2} = \sqrt{\frac{1 - \cos (2 \cdot 22.5)}{2}} \sin \frac{45 °}{2} = \sqrt{\frac{1 - \cos 45 °}{2}} \sin \frac{45 °}{2} = \sqrt{\frac{1 - \frac{1}{\sqrt{2}}}{2}} \sin \frac{θ}{2} = \sqrt{\frac{2 - \sqrt{2}}{2}}$

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Use the Half-angle Formulas to find the exact value of each expression.
$\sin 22.5 °$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value.

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Use the Half-angle Formulas to find the exact value of each expression.sin22.5°.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Mechanics Maths

Statistics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Half-angle Formulas to find the exact value of each expression.
$\sin 22.5 °$ .