Posted by **Joe** on Saturday, July 18, 2009 at 11:10pm.

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

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

- trig -
**Quidditch**, Saturday, July 18, 2009 at 11:41pm
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).

## Answer This Question

## Related Questions

- trig - find the exact solutions 2cos^2x+3sinx=0 the way it stands, that is a "...
- Math (Calc) - Find all solutions to the following equation on the interval 0<...
- trigonometry - Find all solutions on the interval [0.2pi) A) -3sin(t)=15cos(t)...
- trig - Find the exact solutions of the equation in the interval [0,2pi). sin(x/2...
- Math Trig Please Help!!! - Find exact values for all the solutions to the ...
- trig - findall exact solutions ( in terms of radians) to the equation 2cos(40)-...
- Trigonometry - Find all solutions between 0 and 2pi. Round to two decimal places...
- trig - I need to find all solutions of the given equations for the indicated ...
- trig - Find all solutions to the equation 2cos(2x) = x + 1, correct to 4 ...
- trig - Solve the equation for exact solutions over the interval [0, 2pi]. 4 cotx...

More Related Questions