For an angle θ with the point (-20, -21) on its terminating side, what is the value of cosine?

Solution:

The point is (-20, -21) on its terminating side

As both the values are negative it lies on the Quadrant III

We know that the cosine of an angle is the side that is adjacent to the hypotenuse.

First, we have to find the hypotenuse using the Pythagorean theorem

c² = a² + b²

c² = (-20)² + (-21)²

c² = 400 + 441

c² = 841

So we get

c = √841 = 29

Using the trigonometric ratios, we get

cos θ = adjacent/hypotenuse

Substituting the values

cos θ = - 20/29

Therefore, the value of cosine is -20/29.

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For an angle θ with the point (-20, -21) on its terminating side, what is the value of cosine?

Summary:

For an angle θ with the point (-20, -21) on its terminating side, the value of cosine is -20/29.