SOLUTION: Find The value of cos2x if cotx=12/5, where pi

SOLUTION: Find The value of cos2x if cotx=12/5, where pi < x <3pi/2

Question 828965: Find The value of cos2x if cotx=12/5, where pi < x <3pi/2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find The value of cos2x if cotx=12/5, where pi < x <3pi/2
cotx=12/5(working with a (5-12-13) reference right triangle in quadrant III in which sin<0, cos<0
sinx=-5/13
cosx=-12/13
..
cos2x=cos^2x-sin^2x=144/169-25/169=119/169
..
Calculator check:
cosx=-12/13 in quadrant III
x≈202.62
2x≈405.24˚
cos2x≈cos(405.24)≈0.7041..
Exact value as calculated=119/169≈0.7041..
RELATED QUESTIONS
If sinx+cosx=-1/5, and {{{ 3pi/4 }}}≤x≤pi, find the value of... (answered by ikleyn)

if sin x = -1/3 and pi < x < 3pi/2, find the value of sin2x and... (answered by Fombitz)

If {{{ sin x + cos x = -( 1 / 5 ) }}}, and 3pi/4 < or = x < or = pi, find the value of... (answered by ikleyn)

what is the exact value of sin2x, cos2x and tan2x if... (answered by lwsshak3)

If sin(x)= -4/5, on the interval (pi,3pi/2) find the exact value of... (answered by lwsshak3)

If sinx=-5/13 and x is in the interval (pi, 3pi/2), find the exact value of cosx/2 (answered by fcabanski)

If sin(x)+cos(x) = -1/5, and 3pi/4 ≤ x ≤ pi, find the value of... (answered by Edwin McCravy,ikleyn)

If cos x = -(2/3) and pi/2 < x < pi, what is the exact value of sin2x, cos2x, and... (answered by lwsshak3)

Angle x is between (pi,3pi/2) and cos squared x = 10/11. Determine the exact value of... (answered by lwsshak3)