Precalc question pls help?

Question

If sin(theta) =15/17, 0<(And=)theta<(And =)pi/2, then 

cos(theta)=___ 
tan(theta)=___ 
sec(theta)=____

Answer 1

The value of sin(θ) = 15/17 and 0 ≤ θ ≤ π/2.

By using Pythagorean identity sin²(θ) + cos²(θ) = 1, to obtain

(15/17)² + cos²(θ) = 1

cos²(θ) = 1 - (15/17)²

               = 1 - 225/289

               = (289 - 225) / 289

               = 64/289

cos(θ) = ± √(64/289)

cos(θ) = ± 8/17.

The cosine function is positive in first quadrant, so the positive root to obtain

cos(θ) = 8/17.

Quotient Identity : tan(θ) = sin(θ)/cos(θ)

                                                = (15/17) / (8/17)

                                                = 15/8.

Reciprocal Identity : sec(θ) = 1/cos(θ)

                                                = 1 / (8/17)

                                                = 17/8.

The trigonometric values of cos(θ) = 8/17, tan(θ) = 15/8 and sec(θ) = 17/8.