Find the value of cos(θ) for an angle θ in standard position with a terminal Ray that passes through the point (-5,-12)
2 answers:
Answer:
D
Step-by-step explanation:
Let's draw a picture (see attachment).
We know that since our point is (-5, -12), it must pass in the third quadrant. Now, if we drop a perpendicular line from the point (-5, -12) to the x-axis, we have a right triangle. Notice that we already know the two leg lengths of this: -5 and -12.
Cosine is adjacent / hypotenuse. Here, the adjacent side to the angle θ is -5. We need to find the hypotenuse, which we can do so by using the Pythagorean Theorem:
c² = a² + b²
c² = (-5)² + (-12)²
c² = 25 + 144 = 169
c = 13
So, the hypotenuse is 13. Now, plug these values in:
cos(θ) = adjacent / hypotenuse = -5/13
The answer is D.
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