Question

Given that the point (-144, -17) is on the terminal side of an angle, find the exact value of the following:

A. sinθ
B. cosθ
C. tanθ

Answer 1

To find the exact value of sin(theta), cos(theta), and tan(theta), we can use the given point (-144, -17) to determine the values of the trigonometric functions. First, we need to find the hypotenuse of the right triangle formed by the given point. The hypotenuse can be found using the Pythagorean theorem: h = sqrt((-144)^2 + (-17)^2) = sqrt(20785). Next, we can find the values of sin(theta), cos(theta), and tan(theta) by using the ratios of the sides of the triangle: sin(theta) = -17/sqrt(20785), cos(theta) = -144/sqrt(20785), and tan(theta) = -17/-144 = 17/144.

Step-by-step explanation:

To find the exact value of sin(theta), cos(theta), and tan(theta), we can use the given point (-144, -17) to determine the values of the trigonometric functions.

First, we need to find the hypotenuse of the right triangle formed by the given point. The hypotenuse can be found using the Pythagorean theorem: h = sqrt((-144)^2 + (-17)^2) = sqrt(20785).

Next, we can find the values of sin(theta), cos(theta), and tan(theta) by using the ratios of the sides of the triangle: sin(theta) = -17/sqrt(20785), cos(theta) = -144/sqrt(20785), and tan(theta) = -17/-144 = 17/144.