Question

Hi Steve and Damon, if you're reading this, please take a look at my previous post because I had to apologize for my mistake.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ My Home Work Question:

Suppose that α is an angle such that tanα=5/7 and sinα<0. Also, suppose that β is an angle such that cotβ=​−3/5 and cscβ>0. Find the exact value of sine(α−β).

Answer 1

so, use the cos formula, instead of sin. What's the trouble?

cos(α−β) = cosα cosβ + sinα sinβ

You have all the values; just plug 'em in.

Answer 2

As Steve and Damon pointed out to you earlier,
sin(α−β) = sinαcosβ - cosαsinβ

given: tanα=5/7 and sinα<0 , so by the CAST rule
α must be in quadrant III
since tanα = 5/7, by Pythagoras, the hypotenuse of our triangle is √(25+49) = √74
thus sinα = -5/√74 and cosα = -7/√74

similarily, if cotβ=​−3/5 and cscβ>0 , β must be in quadrant II, and tanβ = -5/3
sinβ = 5/√34 , and cosβ = -3/√34

You now have the exact 4 values needed to sub into my formula in the second line.

Answer 3

THANK YOU GUYS SOOO MUCH, GOD BLESS.