Given that cos0=5/13 and 0 lies in the fourth quadrant, find the other five trigonometric function values of 0

Answer 1

This is a SOHCAHTOA problem. I would tackle this problem by drawing an angle in the 4th quadrant and making a right triangle. Since cosθ = 5/13, A = 5 and H = 13. O = -12 since the angle is below the x-axis.

After you have the triangle it is super easy to find all of the trig functions.

sinθ = -12/13

cosθ = 5/13

tanθ = -12/5

cscθ = -13/12

secθ = 13/5

cotθ = -5/12

Answer 2

There are very basic trigonometric identities that you should already know to help you solve this problem:

Pythagorean Identity: sin²(x) + cos²(x) = 1

Reciprocal Identities: csc(x) = 1 / sin(x) , sec(x) = 1 / cos(x), cot(x) = 1 / tan(x)

Quotient Identity: tan(x) = sin(x) / cos(x)

These identities, along with the basic knowledge of which trigonometric quantities are negative in the fourth quadrant, are all you need to solve this problem.