Question

solve 3 sin^2 x - 2 = cos x

Answer 1

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

Answer 2

yes...

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

?

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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.

Answer 16

hmmm okay thanks

Answer 17

welcome :)