I don't understand what this trig problem is asking!!!!!! Can provide more info if needed

Question

If csc(α) = 3, where 0 < α < π/2, and β is a Quadrant II angle with tan(β) = −7, find

 

cos(α+β)

 

And there are others that I'm supposed to find, such as sin(α+β), but this is just the first question.

Answer 1

Sin of any angle is bounded between -1 and 1.  Mark up above left off a denominator when he was calculating for Beta.  (That's really easy to do!)   Use the Pythagorean Theorem to find the denominator  Square Root (49 +1) .

 

So sin β = -7/sqrt(50)   and cos β = 1/sqrt(50)

 

You find the signs by looking at the quadrant the angles are in!

Answer 2

csc α = 3 ⇒ sin α = 1/3, 

tan β = -7 ⇒ sin β / cos β = -7/1 ⇒ sin β = -7 and cos β = 1

 

cos (α + β) = cos α cos β - sin α sin β

 

Now substitute values and calculate