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Hello, I was hoping I could ask for your help on one additional question from my ACT prep booklet worksheets. The question given is:
Question 442
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.

Jonathan, the point (-7,-24) is in the third quadrant where x is -7 and y is -24
If you have a right triangle then let the bottom leg be |-7| = 7 and the other leg |-24| = 24. Now to find the third side, called the hypotenuse and the longest side and the side across from the right angle, use the Pythagorean Theorem that says square one leg, square the second leg, add those two together and then the hypotenuse is the square of the sum of the two legs squared.
(-7)^2 + (-24)^2 = 49 + 576 = 625. 625 can be written as 25^2 so the square root of 625 is 25. Now that you have the measurement of all three sides you can find the sin(theta) and the tan(theta).
Picture your right triangle with the bottom equal to -7 and your vertical side equal to -24, which makes the third side 25. Let theta be the angle on the bottom right where the side of -7 meets the hypotenuse. Draw this picture so you can see what is going on.
In trig the sin of any angle is the side across from theta divided by the hypotenuse and CORRECTION: THE TANGENT OF ANY ANGLE IN A RIGHT TRIANGLE IS THE SIDE ACROSS FROM THE ANGLE DIVIDED BY THE SIDE NEXT TO THE ANGLE. A and in our problem the sin(theta) = -24/25 and tan(theta) = -24/-7= 24/7

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