Hello. Question 3(a) asks for you to evaluate sin(θ), exactly. The 'exactly' bit means no decimal approximation -- they want a ratio. Perhaps you wondered, "How can I do that, without knowing theta?" Turns out, there's a way!

Do you understand the notation tan

^{-1}(θ)? That's the inverse-tangent function, showing theta as the input variable.

Do you remember the right-triangle definitions for trig ratios?

θ goes

__into__ the tangent function, and the trig ratio

Opposite/Adjacent comes

__out__.

What they've shown in the first part of the question is the inverse.

The trig ratio

Opposite/Adjacent goes

__into__ the inverse-tangent function, and

θ comes

__out__.

Therefore,

12/5 is Opposite/Adjacent, in a representative right-triangle containing angle θ (we don't care whatever θ is because we're not asked to find it).

Now, what is the right-triangle definition for sin(θ) ?

Look it up, if you don't know it. Next, draw a right-triangle containing angle θ, and label the appropriate sides 12 and 5. From there, you ought to be able to calculate the information you need to write the exact trig ratio for sin(θ).

If you get stuck again, please show your work thus far. Cheers