SOLUTION: Hello, I was hoping I could ask for your help on one additional question from my ACT prep booklet worksheets. The question given is: Let theta be an angle in standard position.

Question 802598: Hello, I was hoping I could ask for your help on one additional question from my ACT prep booklet worksheets. The question given is:
Let theta be an angle in standard position. If the point (-7,-24) is on the terminal side of theta, find the sin of theta and tan of theta. Express the answers in fraction form with simplified radical form.
Once again, if you could show me your answer and then the guide/steps of how you got that answer (so I can make sure I'm doing it right), I would appreciate it. Sincerely, Johnathan.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Let theta be an angle in standard position. If the point (-7,-24) is on the terminal side of theta, find the sin of theta and tan of theta. Express the answers in fraction form with simplified radical form.
***
use x for theta
reference angle x is in quadrant III where sin<0, cos<0, tan>0.
hypotenuse of reference right triangle=√(7^2+24^2)=√(49+576)=√625=25
cosx=adjacent side/hypotenuse=-7/25
sinx=opposite side/hypotenuse-24/25
tanx=sinx/cosx=-24/-7=24/7
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