SOLUTION: If cos x = sin (20 + x ) degrees and 0 degrees < x < 90 degrees , the value of x is ___ degrees

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Question 1064967: If cos x = sin (20 + x ) degrees and 0 degrees < x < 90 degrees , the value of x is ___ degrees
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
cos x=sin (20+x)
sin (a+b)=sin a* cos b+cos a*sin b
cos x=sin 20*cos x+cos 20*sin x
cos x-sin20*cos x=cos 20* sin x
cos x(1-sin 20)=cos 20* sin x
(1-sin 20)/(cos 20)=sin x/cos x=tan x
(1-.3420)/0.9397=0.6580/0.9397=.7002
arc tan (0.7002)=35 degrees
cos 35=sin (20+x)=0.8192
arc sin (0.8192)=55 degrees
sin (20+x)=sin (55 degrees)
x=35 degrees
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If cos x = sin (20 + x ) degrees and 0 degrees < x < 90 degrees , the value of x is ___ degrees 
cos x = sin (20 + x)

sin and cos are CO-FUNCTIONS, which means that: cos x = cos [90 - (20 + x)]

cos x = cos (90 - 20 - x)

cos x = cos (70 - x)

Therefore, x = 70 - x

x + x = 70

2x = 70

 

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