Question

Find exact values for sin θ, cos θ and tan θ if sec θ = 2 and θ terminates in Quadrant I

What do I do in this situation where it gives a value that is not a fraction? And what are the exact values for sin and cos based off of this? Please provide an explanation.

Answer 1

If the secant theta is 2, then the cosine theta is 1/2. In the first quadrant, with cosine is side adjacent over hypotenuse, then the angle in question is a 60 degree angle. The side opposite the angle is sqrt3. The sin of a 60 degree angle is sqrt3/2 and the tangent is the side opposite over the side adjacent which is sqrt3/1 or just sqrt3.