Question

Suppose that theta is an angle in standard position whose terminal side intersects the unit circle at (-3/5, -4/5). Find the exact values of cos theta, sec theta, and cot theta.

Answer 1

cosθ = -3/5

secθ = -5/3

cosθ = -3/4

Explanation:

To find the exact values of cosθ, secθ, and cotθ, we need to use the given coordinates of the point where the terminal side of θ intersects the unit circle.

The given coordinates are (-3/5, -4/5).

Using the Pythagorean theorem, we can find the value of the radius of the unit circle at this point:

r = √((-3/5)² + (-4/5)²)

= √(9/25 + 16/25)

= √(25/25)

= 1

Now, let's calculate the trigonometric functions:

cosθ = x-coordinate/radius

= (-3/5)/1

= -3/5

secθ = 1/cosθ

= 1/(-3/5)

= -5/3

cotθ = 1/tanθ

= 1/(-4/3)

= -3/4

Therefore, the exact values of cosθ, secθ, and cotθ are:

- cosθ = -3/5

- secθ = -5/3

- cotθ = -3/4