SOLUTION: Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2<x<pi

Question 972617: Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2 ***
cosx=-1/3 (Q2)
sinx=√(1-cos^2(x))=√(1-1/9)=√(8/9)=√8/3
sin(2x)=2sinxcosx=2*√8/3*-1/3=-(2√8)/9
cos(2x)=cos^2(x)-sin^2(x)=1/9-8/9=-7/9
..
check:
cosx=-1/3(Q2)
x≈109.47˚
2x≈218.94˚
..
sin(2x)≈sin(218.94˚)≈-0.6285
exact value as computed=-(2√8)/9≈0.6285
..
cos(2x)≈cos(218.94˚)≈-0.7778
exact value as computed=-7/9≈-0.7778
RELATED QUESTIONS
1)Find the value of t and determine the quadrant cos t= -4/5 2)If the terminal point... (answered by solver91311)

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

1) Find the exact value of (Sin 130*)(cos 132*)+(cos 138*)(sin 132*) 2) Simplify cos... (answered by Edwin McCravy)

sin(x)=8/17 and pi/2 less than x less than pi. Find the exact value of... (answered by stanbon)

Find the exact value of sin((2x),cos(2x) given tan(x)=-9/40, -pi/2 < x < 0 Please... (answered by jsmallt9)

if cos x= -1/4 and pi/2 < x < pi, find the value of... (answered by Tutorteddy.Com)

Question#1: Find the exact value of each of the following. (Hint: you may need Angle... (answered by stanbon)

Find the exact value of each of the following. (Hint: you may need Angle Sum/Difference,... (answered by Alan3354)

If cos x = -2/3 and x terminates in quadrant 2 find the exact value of cos 2x, sin 2x,... (answered by lwsshak3)