given sin=4/5, find cos theta, tan theta, sec theta, and cdc theta. in quadrant 1,2,3,4

Question

for quadrant 2 my professor used sin^2 theta + cos ^2 theta=1 and plugged in (4/5) where sine ^2 is and solved for cosine. Am i supposed to use this formula for every quadrant?

Answer 1

sin is opposite/hypotenuse so adjacent must be 3 if sin=4/5

you have a 3-4-5 right triangle so cos=adj/hyp, cos=3/5, and cos=-3/5 in Q 2

using the trig identity your professor used, (4/5)^2+cos^2=1

16/25+cos^2=1, cos^2=1-16/25, cos^2=9/25, and cos=3/5

You don't you have to use this trig identity if you have all 3 sides of the right triangle. I suppose you could but it seems like more work to do.