# trig

posted by .

how can i find all the exact solutions to the equation : 2cos^2x + 3sinx = 3

the solutions have to be between [0,2pi)

• trig -

assuming that 2cos^2x means 2(cos(x))^2
substitute using
(cos(x))^2 = 1 - (sin(x))^2
2(1 - (sin(x))^2) + 3sin(x) = 3
2 - 2(sin(x))^2 + 3sin(x) = 3
for clarity, let u = sin(x)
2 - 2u^2 + 3u = 3
rearranging...
2u^2 - 3 u + 1 = 0
Solve this quadratic to find the values of sin x that are solutions. Finally, determine the angles in the range that have that value of sin(x).

## Similar Questions

1. ### trig

find the exact solutions 2cos^2x+3sinx=0 the way it stands, that is a "nasty" question. Are you sure the second term isn't 2sin(2x) ?
2. ### Math (Calc)

Find all solutions to the following equation on the interval 0<=x<=2PI 8cos^2(X)sin^2(X) + 2cos^2(X) - 3 = 0 There are 8 solutions. If somebody could show me how to do it and not give me the answers, that would be great.
3. ### trig

I need to find all solutions of the given equations for the indicated interval. Round solutions to three decimal places if necessary. 1.) 3sin(x)+1=0, x within [0,2pi) 2.) 2sin(sq'd)(x)+cos(x)-1=0, x within R 3.) 4sin(sq'd)(x)-4sin(x)-1=0, …
4. ### trig

findall exact solutions ( in terms of radians) to the equation 2cos(40)-radical 3 =0
5. ### trig

Find the exact solutions of the equation in the interval [0,2pi). sin(x/2)+cos(x)=0
6. ### Trigonometry

Find all solutions between 0 and 2pi. Round to two decimal places. In radians. Find all solutions between 0 and 2 pi. Round to two decimal places for the final solutions. The answers should be in radian mode. If you can use exact values …