Solve cos(θ + π/2) if sin θ = 3/7 Exactly

[oddjobmj]

Homework Statement

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

Homework Equations

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

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.

Thank you for your time!

 

[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.

 

[oddjobmj]

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

 

[Mentallic]

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

edit: you would probably realize 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.

 

[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.

 

[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.

 

[oddjobmj]

Haha, that makes me feel a little better :P