# How to solve this problem?

##### 2 Answers

Answer d is correct.

#### Explanation:

I would use identities.

We know that

#(5/13)^2 + cos^2x = 1#

#cos^2x = 1 - 25/169#

#cos^2x = 144/169#

#cosx = +-12/13#

However, we know the answer must be negative because of the C-A-S-T rule, which is shown in the following picture.

So only sine is positive on

Now we can use the quotient identity, which states that

#costheta = x/r#

#sintheta = y/r#

#tantheta = y/x#

Now notice that

#(y/r)/(x/r) = y/x# or#sintheta/costheta = tantheta#

#tantheta = sintheta/costheta = (5/13)/(-12/13) = -5/12#

So answer d.

Hopefully this helps!

#### Explanation:

We know that

So, the opposite and hypotenuse are equal to

For this problem, we can simply consider the opposite and hypotenuse to be

The hypotenuse of a triangle is its longest side.

Using Pythagoras' theorem:

Now,

The interval that we are provided with is

In the second quadrant, all values of

So,

Therefore,

In conclusion, the final answer is