can you help me find cos 2x if sin x = -12/13 (x in 3rd quadrant)
GIVEN: SinX = -12 / 13
SinX = 12/13 = 0.9231, X=67.38(1st.quad.), X = 67.38 + 180 = 247.38
( 3rd. quad, ), Z
2X = 2*247.34 = 494.76
COS2X = COS 494.76 = -0.7041
Yes, I can help you find cos 2x using the given information.
In this case, we only need to find sin x because we know that sin^2 x + cos^2 x = 1.
Since x is in the third quadrant and sin x = -12/13, we can assume that cos x will be negative.
To find cos x, we can use the Pythagorean identity sin^2 x + cos^2 x = 1:
(-12/13)^2 + cos^2 x = 1
144/169 + cos^2 x = 1
cos^2 x = 1 - 144/169
cos^2 x = 25/169
cos x = -5/13
Now, we can use the double-angle formula for cosine to find cos 2x:
cos 2x = 2*cos^2 x - 1
cos 2x = 2*(-5/13)^2 - 1
cos 2x = 2*(25/169) - 1
cos 2x = 50/169 - 1
cos 2x = 50/169 - 169/169
cos 2x = (50 - 169)/169
cos 2x = -119/169
So, cos 2x is equal to -119/169.
Yes, I can help you find cos 2x given that sin x is -12/13 and x is in the third quadrant.
To find cos 2x, we can use the identity:
cos 2x = 1 - 2sin^2 x
Since we already know sin x, we can substitute it into the identity and solve for cos 2x.
Given: sin x = -12/13
cos 2x = 1 - 2(-12/13)^2
First, let's find sin^2 x:
sin^2 x = (-12/13)^2
= 144/169
Now substitute sin^2 x into the identity:
cos 2x = 1 - 2(144/169)
Next, let's simplify the expression:
cos 2x = 1 - (288/169)
To subtract fractions, we need a common denominator, which is 169:
cos 2x = (169/169) - (288/169)
cos 2x = -119/169
Therefore, cos 2x is equal to -119/169.