2 trig questions please help?

think about what sin x and cos x represent in your unit circle.

Is there a point on a circle of radius 1 that more than 1 units away?

or less than 1 unit away?

First question for any real θ, sin(θ) ranges between 1 and -1. Since 5/4 is not in that interval, there is no real θ, that satisfies sin(θ) = 5/4.

Second question, for all real θ, sin²(θ) + cos²(θ) = 1. (.25)² + (.5)² = .0625 + .25 ≠ 1. So you can not have sin(θ) = 0.25 and cos(θ) = 0.5.

if theta is any real number, is it possible for sin(theta) = 5/4? Why or why not?

It is not possible because - 1 </= sin(theta) </= 1

if theta is any real number, is it possible for sin(theta) = 0.25 and cos(theta) = 0.5? Why or why not

It is not possible

If sin(theta) = 0.25 then cos(theta) = Sqrt(3)/4 and

if cos(theta) = 0.5 then sin(theta) = sqrt(3)/2

No. The range of sine is [-1,1].