First slide

Trigonometric equations

Question

The number of integral values of K for which the equation $7 \cos θ + 5 \sin θ = 2 K + 1$ has at least one solution is

Easy

A

8
B

6
C

5
D

4

Solution

The equation $7 \cos θ + 5 \sin θ = 2 K + 1$ has solution if
$\Rightarrow - \sqrt{74} \leq 2 K + 1 \leq \sqrt{74}$
$\Rightarrow - \sqrt{74} - 1 \leq 2 K \leq \sqrt{74} - 1$
$\Rightarrow \frac{- \sqrt{74} - 1}{2} \leq K \leq \frac{\sqrt{74} - 1}{2}$
$\Rightarrow K = - 4, - 3, - 2, - 1, 0, 1, 2, 3$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App