if sin a=-4/5 and cos a>0 find tan a and sec a

Question

I need help with this problem because I do not know how to get started on it.

Answer 1

It is much easier than it initially appears. Remember the definition of SINE:

 

SINΘ = opp             In your case, that means the opposite is 4 (yes, ignore the sign for now) and the hypotenuse is 5.

            hyp             Please draw that triangle right now, because it will help you a lot at the end.

                               Remember to place the angle in the appropriate spot.

Now, use the Pythagorean Theorem to find the missing side (easy, right? It's 3) and place it in the adjacent position.

You can easily find all of the trig functions now!

Simply remember that:

COSΘ = Adj                                  with SEC the reciprocal of this one

             Hyp

TANΘ = Opp                                  COT the reciprocal of TAN and, if anyone asks, CSC coming from SIN.

             Adj

I told you to ignore the signs, but now we can't anymore. Remember the four quadrants and the memory trick:

A                        -- ALL are positive

Smart                 -- SIN and CSC are positive

Trig                    -- TAN & COT are positive

Class                  -- COS and SEC are positive.

Since your SIN was negative, it must be in III or IV, and COS is positive in I & IV. Ahhh, we're in quadrant IV then! 

Only your COS and SEC will be positive, the rest negative.