htpwwwmathl 6450832 Holt McDougal Online Gades and Attendanc

htp//www.mathl 6450832 Holt McDougal Online Gades and Attendance G Gmail PRE-CALCULUS HON-1931 12023400 1007 2016/ Cooper Chy H Test: Chapter 5 Test This Question: 1 pt 90121 (15 complete) The following equation involves a trigonometric equation in quadratic form Solve the equation on the interval 10.2x) 3 sin2x -5 sinx 8 Select the correct choice below and, if necessary, il in the answer box to complete your choice A. or ractions for any numbers in the expression Use a comma to separate answers as needed) (Type an exact answer in terms of K Use integers There is no solution numbers n the expression O B. Click to select and enter your answerls) Type here to search FS F7 d- F4

Solution

3sin^2(x) = -5sinx + 8

3sin^2x + 5sinx - 8 = 0

This is a quadratic in sinx
Let sinx = y

So, 3y^2 + 5y - 8 = 0

a = 3
b = 5
c = -8

Sum = b , prodict = ac becomes
sum = 5
product = -24

So, the two numbers that work are 8 and-3

So, 3y^2 - 3y + 8y - 8 = 0
3y(y - 1) + 8(y - 1) = 0
(3y + 8)(y - 1) = 0
y = -8/3 and 1

So, sinx = -8/3 ----> no solution

sinx = 1 --> has solutin
x = pi/2

So, ans:

x = pi/2 -----> ANS