Chapter 7: Q. 13 (page 485)

Find the exact value of the expression:
$\cos (\frac{7 π}{12})$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

We have been given an expression $\cos (\frac{7 π}{12})$ .

We have to find its exact value.

Step 2. Simplify the expression

We can also write the expression as:

$\cos (\frac{7 π}{12}) = \cos ((\frac{3 π}{12}) + (\frac{4 π}{12})) = \cos ((\frac{π}{4}) + (\frac{π}{3}))$

Step 3. Apply the compound angle formula

$\cos ((\frac{π}{4}) + (\frac{π}{3}))$ has the form role="math" localid="1646467605260" $\cos (α + β)$

Therefore, apply

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

role="math" localid="1646467708680" $\begin{aligned} \cos (\frac{π}{4}) \cos (\frac{π}{3}) - \sin (\frac{π}{4}) \sin (\frac{π}{3}) = ((\frac{\sqrt{2}}{2}) \cdot (\frac{1}{2})) - ((\frac{\sqrt{2}}{2}) \cdot (\frac{\sqrt{3}}{2})) \\ = (\frac{\sqrt{2}}{4}) - (\frac{\sqrt{6}}{4}) \\ = (\frac{\sqrt{2} - \sqrt{6}}{4}) \\ = \frac{1}{4} (\sqrt{2} - \sqrt{6}) \end{aligned}$

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Find the exact value of the expression:
$\cos (\frac{7 π}{12})$

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:cos7π12

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

Statistics

Logic and Functions

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the exact value of the expression:
$\cos (\frac{7 π}{12})$