Question 1156809: if the terminal side of angle thetapasses through point (-3, -4), what is the value of sec theta?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the angle is in the third quadrant because the value of x is -3 and the value of y is -4.
the hypotenuse of the right triangle formed is equal to sqrt((-4)^2+(-3)^2) = sqrt(25) = 5.
the secant of an angle is equal 1 divided by the cosine of the angle.
the cosine of the angle formed is equal to the adjacent side (x-value) divided by the hypotenuse.
that becomes -3/5.
the secant is equal to 1 / the cosine.
this makes it equal to 1 / (-3/5) which is equal to 5 / -3 which is equal to -5/3.
that's your solution.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
if the terminal side of angle thetapasses through point (-3, -4), what is the value of sec theta?
(- 3, - 4) is the same as (cos, sin)
Also, this means that this is a 3-4-5 special right-triangle, which makes the hypotenuse, or r, 5
With cos and sin being < 0,  is in the 3rd quadrant
With cos being negative, sec is also negative
We then get: 
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