# If sin A=2/3 cos B=3/4, angle A is in quadrant 2 and angle B is in quadrant 4. How do you evaluate sin(A-B) without find A and B?

##### 2 Answers

Please see the explanation.

#### Explanation:

Given:

We will need the value of

We are given that A is in the 2nd quadrant, therefore, we chose the negative value for the cosine:

Given:

We will need the

We are given that B is in the 4th quadrant, therefore, we chose the negative value for the sine:

We have all of the values that we need to use the identity:

#### Explanation:

The easiest way I can think of is to use the Pythagorean Identity to first find both

The trigonometric Pythagorean identity tells us that

which follows directly from the geometric identity for right triangles and the fact that

Anyway, if we know

Because we know

Similar reasoning can be done with

Now that we have all the necessary elements, we can use the sum/difference angle identity:

Hope this helps!