You are given that cos(A)=−513, with A in Quadrant III, and sin(B)=513, with B in Quadrant I. Find sin(A−B)

Question

You are given that cos(A)=−513, with A in Quadrant III, and sin(B)=513, with B in Quadrant I. Find sin(A−B)

Answer 1

Hi Kelly P.,

So assuming that Doug C.'s guess is correct, what you need is:

formula for sin (A-B) == sinAcosB - cosAsinB

(It would be a good idea to memorize the sum and difference formulas for sin and cos!)

and also the Pythagorean theorem, to get the "other side" length of the right triangles generated by the specified opened angles.

You should be able to immediately recognize the following two Pythagorean-triples triangles:

3-4-5 and 5-12-13 . (There are an infinite number of them, but these two will appear in your problems a lot!)

You should also be ready to immediately recognize and apply the geometries of 45-45-90 and 30-60-90 triangles.

Once you have sketched your triangles and their directed-side lengths (including + or - signs!!), you can just plug into the sin (A-B) formula and crank.

When you have the skills at that, including the formulas memorized, the sketches and calculation should take you about 1 minute.

--Cheers, --Mr. d.