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What is the value of sinθ given that (5, −12) is a point on the terminal side of θ ?

A. −12/13

B. 12/13

C. −5/13

D. 5/13

Jan 1, 2018

#1
+1

Hi Lexi,

1) To answer this question you first need to graph (-5,12) on the number plane.

2) What quadrant are you in?

3) Is sine positive or negative in this quadrant?

Now sine is opposite/hypotenuse  Hopefully you already know that.

The angle you must use is the one that has one arm on the positive or negative x axis. (whichever will give you an acute angle.

If it is in the 1st or 2nd quad you go up and if it is in the 3rd or 4th quad you go down.

4) Do you know acute angle to use?

5) Now you have a rise, that will definitely be 12 (the y vaue), and you ave a run, that will be 5 (the x vaue) but you will nee to use pythagoras's theorem to work out the hypotenuse.

6) Now you know what sine is.

Jan 1, 2018
#2
+1

(x, y)  =  (5, -12)

And sin   =   y / r

So....we need to find r

r  =  sqrt [ x^2 + y^2]  =  sqrt  [ 5^2  + (-12)^2 ]   =  sqrt  [ 25  +  144 ]  =  sqrt [ 169] = 13

So....sin  =   y / r  =  -12 / 13   Jan 2, 2018