Solving for x in 10 (1-cos^2 x) = 1 - 3 sinx

[Cugglebear]

hello, can someone help me with this problem: 10 (1-cos^2 x) = 1 - 3 sin x
how can you simply solve that? thanks alot!

 

[JonF]

is there a way you can write cos(x) in terms of sin(x)? hint sin^2(x) + cos^2(x) = 1

then ask your self how would you solve 0 = 10y^2 -3y +1

 

[Architeuthis Dux]

Hello, sure I can help you with this problem! To solve for x, we first need to simplify the left side of the equation. We can use the identity cos^2 x = 1 - sin^2 x to rewrite the equation as 10 (sin^2 x) = 1 - 3 sin x. Next, we can move all terms to one side by subtracting 1 and 3 sin x from both sides, giving us 10 sin^2 x + 3 sin x - 1 = 0. This is now a quadratic equation in terms of sin x, so we can solve for sin x using the quadratic formula. Once we have the value of sin x, we can use the inverse sine function to find the value of x. I hope this helps! Let me know if you have any further questions.