Question

Find cos(a + b) if sin(a) = -8/17 where a is in the fourth quadrant and tan(b) = -20/21 where b is in the second quadrant.

Answer 1

Are you allowed to use a calculator?

Answer 2

It's multiple choice - sometimes they want fractions, and sometimes they want decimals.

Answer 3

But in the test, yes, I'm allowed to use a calculator.

Answer 4

Finding the cosine of a is easy enough, but to find the sine and cosine b, do I use 1+tan^2b=sec^2b?

Answer 5

If you are allowed a calculator, there is another way to go about solving these problems, rather than using the "sum of angles" formulas. Are you supposed to use the sum of angles?
e..g cos(a+b)= cos(a)cos(b)-sin(a)sin(b)

Answer 6

Yeah, using the pythag identities is the purpose of this lesson, but it would certainly be helpful if I knew another way to do these.

Answer 7

first step, sketch the angles in the correct quadrant, and label the sides based on the info they give.

Answer 8

yes, you may use the cos(a+b) = cos(a)cos(b) - sin(a)sin(b). but, before that, you may draw it like this., a is in the fourth quadrant, so opposite side is negative. b, is in the second quadrant, so adjacent side is negative, opposite side is positive.