SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −1/6, cos x > 0
sin 2x =
cos 2x =
tan 2x =
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Question 967184: Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −1/6, cos x > 0
sin 2x =
cos 2x =
tan 2x =
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −1/6, cos x > 0
reference angle x is in quadrant IV where cos>0, sin<0
hypotenuse of reference right triangle in quadrant IV=√(6^2+1^2)=√(36+1)=√37
sinx=-1/√37=-√37/37
cosx=6/√37=(6√37)/37
..
sin(2x)=2sinxcosx=2*-√37/37*6√37/37=-444/1369
cos(2x)=cos^2(x)-sin^2(x)=36/37-1/37=35/37
tan(2x)=sin(2x)/cos(2x)=16428/47915
..
Check:
tanx=1/6(Q4)
x=350.538
2x=701.075
..
sin(2x)=sin(701.075)=-0.3243
exact value as computed=-444/1369≈-0.3243
..
cos(2x)=cos(701.075)=0.9459
exact value as computed=35/37≈0.9459
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