# finding exact values trig: Suppose θ = tan^{-1}(12/5). Find the exact value of sin(θ)

#### hildaburger

##### New member
hi I am struggling to figure out what this question wants me to do?

3. Suppose θ = tan-1(12/5). Find the exact value of​
(a) sin(θ)​

#### Otis

##### Senior Member
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 