SOLUTION: 3cos (x+30°)/2 + 2sin^2 (x+30°)/2 = 3 find x?

Algebra ->  Trigonometry-basics -> SOLUTION: 3cos (x+30°)/2 + 2sin^2 (x+30°)/2 = 3 find x?       Log On


   

Question 801801: 3cos (x+30°)/2 + 2sin^2 (x+30°)/2 = 3


find x?







Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
3cos (x+30°)/2 + 2sin^2 (x+30°)/2 = 3
find x?
***
let u=(x+30˚)
3cosu/2+2sin^2u/2=3
3cosu/2+sin^2u=3
3cosu/2+(1-cos^2u)=3
LCD:2
3cosu+2-2cos^2u=6
2cos^2u-3cosu-4=0
solve for cosu by quadratic formula:
cosu+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2, b=3, c=-4
ans:
cosu=2.351 (reject, -1 < cosu < 1)
or
cosu=-0.851
u≈148˚and 212˚ in quadrants II and III where cos<0
..
x+30=148
x=148-30=118˚
or
x+30=212
x=212-30=182˚