# How do you determine #tantheta# given #sectheta=-5/4, 90^circ<theta<180^circ#?

##### 1 Answer

#### Answer:

Please see the explanation.

#### Explanation:

Here is how you derive a relationship between

Start with

Divide both sides by

Substitute

Substitute

Subtract 1 from both sides:

square root both sides:

You do not need to remember this, because it is so easily derived.

Now that we have derived the equation for

Because we are told that the angle is in the second quadrant, we know that the tangent function is negative so we drop the + sign: