SOLUTION: Suppose sinθ=x/4 and the angle θ is in the first quadrant. Write algebraic expressions for cos(θ) and tan(θ) in terms of x.

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose sinθ=x/4 and the angle θ is in the first quadrant. Write algebraic expressions for cos(θ) and tan(θ) in terms of x.      Log On


   

Question 917709: Suppose sinθ=x/4 and the angle θ is in the first quadrant. Write algebraic expressions for cos(θ) and tan(θ) in terms of x.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28theta%29%5E2%2Bcos%28theta%29%5E2=1
x%5E2%2F16%2Bcos%28theta%29%5E2=1
cos%28theta%29%5E2=1-x%5E2%2F16
cos%28theta%29=0+%2B-+sqrt%281-x%5E2%2F16%29
Since theta is in the first quadrant, cos%28theta%29%3E=0,
so,
cos%28theta%29=sqrt%281-x%5E2%2F16%29
and
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29
tan%28theta%29=%28x%2F16%29%2F%28sqrt%281-x%5E2%2F16%29%29
tan%28theta%29=x%2F%284%2Asqrt%2816-x%5E2%29%29%29