# Evaluate sin(theta)

1. May 8, 2010

### oddjobmj

1. The problem statement, all variables and given/known data

Evaluate cos(θ + π/2) if sin θ = 3/7, exactly.

2. Relevant equations

How do I go about doing this exactly instead of approximately on the calculator?

3. The attempt at a solution

The only way I know how to do it is taking the inverse sin of 3/7 and adding 90 degrees and taking the cos of that result.

2. May 8, 2010

### rock.freak667

If sin θ = 3/7 and sin θ = opposite/hypotenuse, can you draw a right angled triangle, with an angle θ, with the opposite side as 3 and the hypotenuse as 7 and find what cosθ is?

What do you get when you expand out cos(θ + π/2)?

EDIT: expand out cos(θ + π/2) first and then see what quantities you need to find.

3. May 8, 2010

### oddjobmj

Wow, way easier than I was letting it be. Thank you!

4. May 8, 2010

### Mentallic

Or use the fact that $$cos(\theta+\pi/2)=-sin\theta$$

edit: you would probably realise this after expanding the cosine, but if you didn't know how to, using the known graphs of cosx and sinx can give you that result easily.

5. May 8, 2010

### oddjobmj

I appreciate the reference there Mentallic! The issue I'm having is, unfortunately, a lack of time to memorize certain equations and equivalents for an exam.

6. May 9, 2010

### Mentallic

Oh yes of course I never expected you to remember this result. I didn't even have this memorised, I had to graph $cos(x+\pi/2)$ to see what it was equivalent to.

7. May 9, 2010

### oddjobmj

Haha, that makes me feel a little better :P