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

Algebra ->  Trigonometry-basics -> SOLUTION: 7 sin^2x - 14 sin x + 2 = -5      Log On


   

Question 1073767: 7 sin^2x - 14 sin x + 2 = -5
Found 3 solutions by Fombitz, ikleyn, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=sin%28x%29
7u%5E2-14u%2B2=-5
7u%5E2-14u%2B7=0
u%5E2-2u%2B1=0
%28u-1%29%5E2=0
u-1=0
u=1
sin%28x%29=1
x=%28%282n%2B1%29%2F2%29%2Api where n is any integer.

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
7 sin^2x - 14 sin x + 2 = -5   <--->

7*(sin^2(x) - 2sin(x) +1) = 0  <---->

%28sin%28x%29-1%29%5E2 = 0,  <---->

sin(x) = 1  --->  x = pi%2F2+%2B+2k%2Api,  k = 0, +/-1, +/-2, . . .


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
7 sin^2 x - 14 sin x + 2 = -5
:
subtract 2 from both sides of =
:
7 sin^2 x - 14 sin x = -7
:
divide both sides of = by 7
:
sin^2 x - 2 sin x = -1
:
sin^2 x - 2 sin x + 1 = 0
:
factor the quadratic
:
(sin x - 1)^2 = 0
:
sin x = 1
:
*******************************************************
x = 90 + ( 2 * 180 * n) where n belongs to the integers(Z)
*******************************************************
: