Solve the following. Find all solutions from 0 degrees to 360 degrees.

1. 4 sin^2 x – 1 = 0

2. sin^2 x + sin x = 1

Guest Apr 17, 2019

#1**+1 **

1. 4 sin^2 x – 1 = 0 add 1 to both sides

4sin^2x = 1 divide both sides by 4

sin^2 x = 1/4 take both roots and we have that

sin x = √[1/2 ] and this happens at 45 degrees and 135 degrees

And

sin x = - √[1/2] and this happens at 225 degrees and 315 degrees

CPhill Apr 17, 2019

#2**+1 **

2. sin^2 x + sinx = 1

sin^2 x + sin x - 1 = 0

Let a = sin x

a^2 + a - 1 = 0

a^2 + a= 1 complete the square on a

a^2 + a + 1/4 = 1 + 1/4

(a + 1/2)^2 = 5/4

Take both roots

a + 1/2 = √5/2

a = √5 - 1

_____

2

sin x = √5 - 1

_____ take the arcsin and x ≈ 38.17° and (180 - 38.17) ≈ 141.8°

2

Or

a = -√5 + 1

______

2

sin (x) = - √5 - 1

_______ this answer is < -1....so no answer for sin x

2

CPhill Apr 17, 2019