91.2k views
3 votes
Find the value of cos(θ) for an angle θ in standard position with a terminal Ray that passes through the point (-5,-12)



Find the value of cos(θ) for an angle θ in standard position with a terminal Ray that-example-1
User Liloka
by
8.8k points

2 Answers

5 votes

Answer:

d. -5/13

Explanation:

Hypotenuse = sqrt(5² + 12²) = 13

|cos(theta)| = 5/13

Since the angle is in quadrant 3, cos will be negative

Therefore, cos(theta) = -5/13

User Berserker
by
7.8k points
4 votes

Answer:

D

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.

Find the value of cos(θ) for an angle θ in standard position with a terminal Ray that-example-1
User Sleeparrow
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories