Posted by **bandit** on Wednesday, January 12, 2011 at 6:31pm.

how do i solve this equation algebraicly

solve the equation 1+25cos(x)=25sin^2(x)

- pre-calc -
**MathMate**, Wednesday, January 12, 2011 at 7:01pm
Substitute sin²(x)=1-cos²(x).

This results in a quadratic equation in cos(x). Solve for y=cos(x) and evaluate x=arccos(y) if -1≤y≤1.

- pre-calc -
**helper**, Wednesday, January 12, 2011 at 7:07pm
1+25cos(x)=25sin^2(x)

-25 sin^2 x + 25 cos x + 1

-25 (1 - cos^2 x) + 25 cos x + 1

-25 + 25 cos^2 x + 25 cos x + 1

25 cos^2 x + 25 cos x - 24

substitute u = cos x

25u^2 + 25u - 24

complete the square

u^2 + u - 24/25 = 0

u^2 + u = 24/25

u^2 + u + 1/4 = 121/100

(u + 1/2)^2 = 121/100

take square root of both sides

| u + 1/2 | = 11/10

u + 1/2 = -11/10 and u + 1/2 = 11/10

u = -8/5 and u = 3/5

substitute back in u = cos x

cos x = -8/5 and cos x = 3/5

x = arccos (-8/5)

x = arccos (3/5)

- pre-calc -
**helper**, Wednesday, January 12, 2011 at 7:15pm
forgot to put

I am not a tutor

I think this is right

- pre-calc -
**MathMate**, Wednesday, January 12, 2011 at 8:22pm
It's almost perfect.

In the last step,

"x = arccos (-8/5)

x = arccos (3/5) "

we have to reject the first value of arccos(-8/5) because arccos(-8/5) does not exist.

For a solution between 0 and 2π, there are two values of x that satisfy arccos(3/5), i.e.

approx. 53 degrees and 360-53 degrees.

For the general solution, add 2kπ to the solutions, where k is an integer.

## Answer this Question

## Related Questions

- Pre-Calc - I need to figure out how to solve the equation x-squared y-squared+xy...
- Pre-Calc - To solve an equation by finding x-intercepts, Cynthia graphed the ...
- confused calc - dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=? (you already...
- Pre-Calc - How do I solve this equation? 4^x * (1/2)^3-2x = 8*(2^x)^2
- Pre-Calculus - Solve the equation 2x + 5y - 3z = -1. Write the general solution ...
- Pre-Calc - How do I solve this equation? x+5 = sqrt(x+5)
- Pre-Calc - Solve the equation. (tan^2)3x=3
- Trig/Pre-Calc - Could someone please help me on this problem. I'm really ...
- pre calc - solve the equation 1+4sin(x)=4cos^2(x)
- calc - What are the intercepting points of y^2=-4x and x^2=y I set both ...

More Related Questions