Question

MEDALS WILL BE REWARDED!! HELP!!
Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

That is sin(2x) or sin^2(x)?

Answer 2

sin2x
so yes
sin(2x)

Answer 3

@Psymon help?

Answer 4

You sure its not sin squared? O.o

Answer 5

hahaha its is sin squared

Answer 6

sorry @Psymon

Answer 7

Okay, that makes wayyyy more sense then o.o Okay then yeah, treat this like a quadratic. Instead of x^2, x, number, we have sin^2, sin, number. So what I can do is set everything equal to 0 and factor out a 7. Doing this leaves us with:
\[7(\sin ^{2}x-2sinx+1)=0\]So this is basically the same as if it were:
\[7(x ^{2}-2x+1)=0\]
Would you know how to factor that?

Answer 8

x=0,1,2?

Answer 9

Well this factors to 7(x-1)(x-1) = 0. Do you see how?

Answer 10

yes i do.... so my

Answer 11

zeros would be 1 and 0?

Answer 12

Just 1. But since we're dealing with sinx and not actually x, we have 7(sinx-1)(sinx-1) = 0
Meaning we have to solve sinx = 1.

Answer 13

and how do we do that?

Answer 14

Well, it requires knowledge of the unit circle. With values like 0 and 1, though, they are a little bit easier to find even if you don't know theunit circle that well. So cosine refers to x values and sin refers to y values, and a unit circle is a circle with a radius of 1.




So given that sin is a y coordinate, where on that circle is the y-coordinate equal to 1?