SOLUTION: Find sin (2x), cos (2x), and tan (2x) from the given information. sec (x) = 10 x in quadrant 4

Question 810474: Find sin (2x), cos (2x), and tan (2x) from the given information.
sec (x) = 10
x in quadrant 4
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.
sec (x) = 10, x in quadrant 4
***
secx=10=1/cosx
cosx=1/10
sinx=√(1-cos^2x)=√(1-1/100)=√(99/100)=-√99/10
tanx=sinx/cosx=√99/1=-√99
..
sin(2x)=2sinxcosx=2*-√99/10*1/10=-2√99/100=-√99/50
cos(2x)=cos^2x-sin^2x=1/100-99/100=-98/100=-49/50
tan(2x)=2tanx/1-tan^2x=2*-√99/(1-99)=-2√99/-98=√99/49
...
Check(w/calculator)
cosx=1/10(in quadrant IV where cos>0
x=275.7392
2x=551.478
..
sin(2x)=sin(551.4783)≈-0.1989..
Exact answer=-√99/50≈-0.1989..
..
cos(2x)=cos(551.4783)≈-0.9800..
Exact answer=-49/50≈-0.9800..
..
tan(2x)=tan(551.4783)≈0.2031..
Exact answer=-49/50≈0.2031..
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