Question

If 0 is an angle in standard position and its terminal side passes through the point

(-7,24), find the exact value of sec 0 in simplest radical form.

Answer 1

The exact value of sec θ in simplest radical form is 25/7.

Step-by-step explanation:

To find the exact value of sec θ in simplest radical form, we need to determine the cosine of θ.

Since the terminal side of θ passes through the point (-7,24), we can calculate the hypotenuse of the right triangle formed by the coordinates as √((-7)^2 + 24^2) = 25.

Using the Pythagorean theorem, we can find the adjacent side as 7. Hence, cos θ = adjacent/hypotenuse = 7/25.

Now, sec θ is the reciprocal of cos θ. So, sec θ = 1/cos θ = 1/(7/25) = 25/7.