Chapter 7: Q. 12 (page 485)

Find the exact value of the expression:
$\sin (\frac{π}{12})$

Short Answer

Expert verified

$\frac{1}{4} (\sqrt{6} - \sqrt{2})$ .

Step by step solution

Step 1. Given information

We have been given an expression $\sin (\frac{π}{12})$ .

We have to find its exact value.

Step 2. Simplify the expression

We can also write the expression as:

$\sin (\frac{π}{12}) = \sin ((\frac{3 π}{12}) - (\frac{2 π}{12})) = \sin ((\frac{π}{4}) - (\frac{π}{6}))$

Step 3. Apply the compound angle formula

$\sin ((\frac{π}{4}) - (\frac{π}{6}))$ has the form $\sin (α - β)$

Therefore, apply

$\sin (α - β) = \sin α \cos β - \cos α \sin β$

$\begin{aligned} \sin (\frac{π}{4}) \cos (\frac{π}{6}) - \cos (\frac{π}{4}) \sin (\frac{π}{6}) = ((\frac{\sqrt{2}}{2}) \cdot (\frac{\sqrt{3}}{2})) - ((\frac{\sqrt{2}}{2}) \cdot (\frac{1}{2})) \\ = (\frac{\sqrt{6}}{4}) - (\frac{\sqrt{2}}{4}) \\ = (\frac{\sqrt{6} - \sqrt{2}}{4}) \\ = \frac{1}{4} (\sqrt{6} - \sqrt{2}) \end{aligned}$

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Find the exact value of the expression:
$\sin (\frac{π}{12})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression

Step 3. Apply the compound angle formula

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Find the exact value of the expression:sinπ12

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression

Step 3. Apply the compound angle formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Applied Mathematics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Find the exact value of the expression:
$\sin (\frac{π}{12})$