## shaqadry 2 years ago solve 3 sin^2 x - 2 = cos x

1. tyteen4a03

Remember that $$sin^2(x) + cos^2(x) = 1$$.

yes...

3. ashwinjohn3

Is 3 sin^2(x-2)=cos x

4. tyteen4a03

@ashwinjohn3 I believe it's 3sin^2(x) - 2.

yea its 3 sin^2 (x) - 2 = cos (x)

6. hartnn

change sin^2 x to cos^2 x using $$\sin^2(x) + \cos^2(x) = 1$$ then if you put cos^2 x = y, you'll get a quadratic in y.

7. ashwinjohn3

ok... then,here $\sin ^{2} x=1-\cos ^{2} x$ $3 (1-\cos ^{2}x )-2=3-3 \cos ^{2}x -2=1-3\cos ^{2}x$

thats what i get but then i cant figure out how to solve the angle :/

9. hartnn

put cos x =y, then you get a quadratic in y..

10. ashwinjohn3

But $1=\cos ^{2}x+\sin ^{2} x$ =$\sin ^{2}x+\cos ^{2}x-3\cos ^{2}x=\sin ^{2}x-2\cos ^{2}x$

11. hartnn

?

12. hartnn

$$3 \sin^2 x - 2 = \cos x \\ 1-3\cos^2x = \cos x \\ 1-3y^2 =y. \\ 3y^2 +y-1=0$$ can you solve this quadratic ?

yeaaa but by using calculator, the answer is in decimal point. is there any other way i can calculate the angle?

14. hartnn

you'll get same answer using any other method, that you got on calculator. whatever you got, equate it to y= ..., ... so, cos x = ... , .... then take cos^{-1} (or arccos) of those 2 values ("decimal values"), using calculator, and ou'll get 2 angles.

15. hartnn

you might be getting, -0.767 and 0.434 then 2 angles will be cos^{-1}(-0.767) and cos^{-1}(0.434) calculate those using calculator.

hmmm okay thanks

17. hartnn

welcome :)