Tanθ = 5/12 , with θ in Quadrant 1, find sin2θ?

[Neopets]

Homework Statement

Tanθ = 5/12 , with θ in Quadrant 1, find sin2θ?

Homework Equations

The Attempt at a Solution

I drew a diagram in quadrant 1, it pretty much looked like a right triangle with a 5 for the length of the sin part and the 12 for the length of the cos part of the tan of 5/12 mentioned in the initial question. Then I noted that sin will be positive in the first quadrant. Now I'm having trouble coming up with the formula to use, I tried Sin2θ=2sinθcosθ which did not work.

 

[Strants]

What exactly are you using for sine and cosine in the equation? Keep in mind, sine and cosine cannot be less than -1 or greater than 1. 5/12 is the proportion, but that does not mean $\sin(\theta)=5$.

It might be helpful to consider the definition sine=opposite/hypotenuse. The opposite side of your triangle is 5, as you know. What is the hypotenuse?

 

[cosmoKaty]

the triangle is 5, 12, 13

cos(theta) = adj/hyp
sin(theta) = opp/hyp
x2= ?

 

[Mark44]

the triangle is 5, 12, 13

cos(theta) = adj/hyp
sin(theta) = opp/hyp

So cos(θ) = ?
And sin(θ) = ?
You have all the numbers you need to figure these out. Once you get them, you can get sin(2θ) by using the double angle identity.

x2= ?

It's customary to write two times a variable with the constant first, as in 2x. In any case, your variable is θ, so it would be 2θ. If you write x2 or θ2, people are liable to think you're trying to write x² or θ², or that you have a variable named x₂.

 

[cosmoKaty]

okay sorry about that, I meant "times two"
would that have been the correct next step?

 

[Strants]

Can you find $\sin(\theta)$ and $\cos(\theta)$? If so, you can use the double angle identity for sine to find the answer.

 

[Mark44]

okay sorry about that, I meant "times two"
would that have been the correct next step?

No. The steps are laid out in my post and in Strants's post.