Question

Suppose that is an angle in standard position whose terminal side intersects the

unit circle at (20/29, -21/29)
Find the exact values of sec θ, tan θ, and sin θ.

Answer 1

The exact values of sec θ, tan θ, and sin θ are 29/20, -21/20, and 21/29 respectively.

Step-by-step explanation:

To find the exact values of sec θ, tan θ, and sin θ, we first need to determine the values of cos θ and θ.

Given that the terminal side of the angle intersects the unit circle at (20/29, -21/29), we can use the Pythagorean theorem to find the value of cos θ:

cos θ = x-coordinate = 20/29

Next, we can use the quadrant in which the terminal side lies (quadrant IV) to determine the value of θ:

θ = tan-1(y-coordinate/x-coordinate) = tan-1((-21/29)/(20/29)) = tan-1(-21/20)

Now that we know cos θ and θ, we can calculate the exact values of sec θ, tan θ, and sin θ:

sec θ = 1/cos θ = 1/(20/29) = 29/20

tan θ = sin θ/cos θ = (-21/29)/(20/29) = -21/20

sin θ = √ (1 - cos2 θ) = √ (1 - (20/29)2) = √ (1 - 400/841) = √ (441/841) = 21/29