SOLUTION: Solve for 'x' 0=Cos^2(x)-2Sinx

Question 248490: Solve for 'x'
0=Cos^2(x)-2Sinx
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve for 'x'
0=Cos^2(x)-2Sinx
-----------------
cos^2(x) = 1 - sin^2(x)
------------------------------
Equation:
0 = 1-sin^2(x) - 2sin(x)
---
= 0Rearrange:
sin^2(x) + 2sin(x) -1 = 0
---
This is a quadratic with a=1; b = 2 ; c = -1
---------------------------------------------------
sin(x) = [-2 +- sqrt(4 - 4*1*-1)]/2
---
sin(x) = [-2 +- sqrt(8)]/2
---
sin(x) = [-2 +- 2sqrt(2)]/2
---
sin(x) = [-1 + sqrt(2)] or sin(x) = [-1-sqrt(2)]
---
Since -1<= sin(x) <= 1, only sin(x) = -1+sqrt(2) is a solution:
---
sin(x) = -1 + 1.414 = 0.4142
-------------------------------
x = sin^-1(0.4142) = 24.47 degrees
====================================
Cheers,
Stan H.
RELATED QUESTIONS
solve for x.... (answered by Fombitz)

Solve for x. 2sinx + 2tanx =... (answered by ikleyn)

solve cos2x-2sinx-cos^2 x = -3 on the interval x ∈... (answered by MathLover1)

Solve the equations of [0, 2pi]: cosx(2sinx-1)=0 and... (answered by lwsshak3)

Hi, can you please help me with this question; Solve the following equation for x <_ x <_ (answered by lwsshak3)

solve 2sinx-1= 0 for 0 is less than or equal to x less than 2pi (answered by god2012)

Solve for (0<=x<=360) sin2x-cosx=-1+2sinx... (answered by Alan3354,ikleyn)

Solve for all solutions for... (answered by Fombitz)

solve for all values of x 1. sec^2x-2=0 2. csc6x+2=0 3.... (answered by stanbon)