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Chapter 7: Q. 93 (page 487)

solve each equation on the interval
$0 \leq θ < 2 π$
$\sin θ + \cos θ = \sqrt{2}$

Short Answer

Expert verified

$θ = 2 n π + \frac{π}{4}$

Step by step solution

01

Step 1. The information given is

a trignometric equation

$\sin θ + \cos θ = \sqrt{2}$

02

Step 2.Multiplying equation by 12

$\sin θ \sin (\frac{π}{4}) + \cos θ \cos (\frac{π}{4}) = 1 \cos (θ - \frac{π}{4}) = \cos (0)$

03

Step 3. The general equation we get is

$θ = 2 n π + \frac{π}{4}$

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Most popular questions from this chapter

Express the product $\sin (3 θ) \sin (5 θ)$ as a sum containing only sines or only cosines.

Find the exact value of the expression:

$\sin 195 ° \cdot \cos 75 °$

solve each equation on the interval

$0 \leq θ \leq 2 π$

$\sin θ - \cos θ = - \sqrt{2}$

express each product as a sum containing only sines or only cosines

$\sin ϑ \sin 2 ϑ$

True or False:

$\tan 2 θ + \tan 2 θ = \tan (4 θ)$

See all solutions

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