SOLUTION: Please help me Solve the following equation for x, if 0 ≤ x ≤ 2π a) 2cosēθ + cosθ - 1 = 0 b) sinēθ - sinθ = 0 c) √58cos(&#95

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me Solve the following equation for x, if 0 ≤ x ≤ 2π a) 2cosēθ + cosθ - 1 = 0 b) sinēθ - sinθ = 0 c) √58cos(&#95      Log On


   



Question 750034: Please help me
Solve the following equation for x, if 0 ≤ x ≤ 2π
a) 2cosēθ + cosθ - 1 = 0
b) sinēθ - sinθ = 0
c) √58cos(θ + 0.78) = -6
Thanks

Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following equation for x, if 0≤ x ≤ 2π
a) 2cosēθ + cosθ - 1 = 0
(2cosx-1)(cosx+1)=0
cosx=1/2
x=π/3, 5π/3
or cosx=-1
x=π
..
b) sinēθ - sinθ = 0
sinx(sinx-1)=0
sinx=0
x=0,π
sinx=1
x=π/2
..
c) √58cos(θ + 0.78) = -6
cos(x+.78)=-6/√58≈-0.79
cos^-1(-0.79)≈2.48 in Q2
x+.78=2.48
x=2.48-.78=1.7

Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Look at #a.


First, let w=cos%28theta%29, then 2w%5E2%2Bw-1=0
w=%28-1%2B-+sqrt%281-4%2A2%2A%28-1%29%29%29%2F%282%2A2%29
w=%28-1%2B-+3%29%2F4
w=-1 or w=1%2F2

Reverse the substitution.
cos%28theta%29=-1 or cos%28theta%29=1%2F2

highlight%28theta=pi%29 or highlight%28theta=pi%2F3%29, or also 5%2Api%2F3