Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

Question

Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

anonymous · Answer

pi/2?

anonymous · Answer

ok how do i solve this question?

campbell_st · Answer

add 7 to both sides of the equation 

so you have

$$7\sin^2(x) - 14\sin(x) + 7 = 0$$

divide each term by 7

$$\sin^2(x) -2\sin(x) + 1 = 0$$

this is a quadratic equation the factorises to a perfect square

hope this helps

anonymous · Answer

ok thank you guys

campbell_st · Answer

oops should have been add 5

anonymous · Answer

Wait you're both giving me two different equations i'm confused.

campbell_st · Answer

the correct equation occurs by adding 5 to both sides of the equation

$$7\sin^2(x) - 14\sin(x) + 7 = 0$$

anonymous · Answer

No confusion now.
I getting out while the getting is good.
Sorry about that.

anonymous · Answer

ok so once i have 7sin2(x)−14sin(x)+7=0
can you help me factor it please because the sin throws me off a bit

campbell_st · Answer

ok... divide each term by 7

campbell_st · Answer

to make it easy let u = sin(x)

so you have 

$$u^2 - 2u + 1 = 0$$

can you factor this... its a perfect square

anonymous · Answer

(u-1)(u-1)?

campbell_st · Answer

yep... or (u -1)^2 = 0

reverse the substitution 

(sin(x) -1)^2 = 0

so you need to solve 

sin(x) -1 = 0

hope that makes sense

anonymous · Answer

ok i understand the factoring now. so i would get sinx=1?

campbell_st · Answer

you will... to you need to find  

$$x = \sin^{-1}(1)$$

anonymous · Answer

Wait im confused how did you get
 x=sin^-1(1)

campbell_st · Answer

its the arcsin.... or what angle gives sin a value of 1. 

its 90 degrees or pi/2

anonymous · Answer

oh ok

anonymous · Answer

thank you for your help:)

campbell_st · Answer

hope it makes sense

anonymous · Answer

its a bit easier now thank you