Question

Find the exact values of the six trigonometric functions of θ for the given coordinates.

(3, -4)
(-1, 2)
(-1, -1)
(5, 12)
A) The question is incomplete and cannot be answered with options.
B) The exact values for the trigonometric functions are provided for each set of coordinates.
C) The exact values of the trigonometric functions depend on additional information not provided.
D) The exact values of the trigonometric functions cannot be determined without knowing the angles θ.

Answer 1

To find the exact values of the trigonometric functions of θ for the given coordinates, use the concepts of trigonometry and the ratios of the sides of a right triangle.

Step-by-step explanation:

To find the exact values of the six trigonometric functions of θ for the given coordinates, we need to use the concepts of trigonometry. The trigonometric functions are defined in terms of the ratios of the sides of a right triangle.

First, we need to determine the lengths of the sides of the right triangle formed by the given coordinates. For example, for the coordinates (3, -4), the length of the adjacent side is 3 and the length of the opposite side is -4.

Using these values, we can find the exact values of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) by dividing the appropriate side lengths. For example, sinθ = opposite/hypotenuse = -4/5.