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
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
