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Chapter 7: Q. 29 (page 505)

Solve each equation on 0鈮�胃<2蟺.

4sin2胃+7sin胃=2

Short Answer

Expert verified

The solutions are 胃=0.253,2.889.

Step by step solution

01

Step 1. Given Information  

We are given the equation 4sin2胃+7sin胃=2and we need to find the solutions of the equation on the interval 0鈮�胃<2蟺.

02

Step 2. Simplifying the equation  

Factorizing the equation we get,

4sin2胃+7sin胃=2鈬�4sin2胃+7sin胃-2=0鈬�4sin2胃+8sin胃-sin胃-2=0鈬�4sin胃(sin胃+2)-1(sin胃+2)=0鈬�(4sin胃-1)(sin胃+2)=0

03

Step 3. Finding the solutions

When

4sin胃-1=0鈬�4sin胃=1鈬�sin胃=14

In the interval [0,2蟺), 胃={0.253,2.889}.

When

sin胃+2=0鈬�sin胃=-2

Since value of 胃ranges between 0and 1in this interval. There is no solution for 胃when sin胃=-2

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