Question

"For the angle's terminal side passing through (6, -4), find the following function values:

a) Sinθ =
b) Cosθ =
c) Tanθ =
d) Cotθ ="

Answer 1

To find the function values of sin, cos, tan, and cot for the given angle's terminal side, we can use the ratios involving the sides of the right triangle formed by the angle.

Step-by-step explanation:

To find the function values of sin(theta), cos(theta), tan(theta), and cot(theta) for the angle's terminal side passing through (6, -4), we need to determine the ratios involving the sides of the right triangle formed by the angle.

Let's label the sides of the triangle as follows:

• The adjacent side is 6
• The opposite side is -4
• The hypotenuse can be found using the Pythagorean theorem: hypotenuse = sqrt(6^2 + (-4)^2) = sqrt(36 + 16) = sqrt(52) = 2sqrt(13)

Now we can calculate the function values:

• sin(theta) = opposite/hypotenuse = -4/(2sqrt(13)) = -2sqrt(13)/13
• cos(theta) = adjacent/hypotenuse = 6/(2sqrt(13)) = 3sqrt(13)/13
• tan(theta) = opposite/adjacent = -4/6 = -2/3
• cot(theta) = 1/tan(theta) = 1/(-2/3) = -3/2