Question

Given that p=(3,-7) is a point on the terminal side of an angle a, find each of the six trigonometric functions of a. Round to the nearest thousandth. 1. sin(a) equals [a] 2. cos(a) equals [b] 3. tan(a) equals [c] 4. cot(a) equals [d] 5. sec(a) equals [e] 6. csc(a) equals [f]

Answer 1

To find the trigonometric functions of angle a for the point (3,-7), we can use the coordinates to calculate the values. The values for sine, cosine, tangent, cotangent, secant, and cosecant can be found by using the given point's coordinates.

Step-by-step explanation:

To find the trigonometric functions of angle a, we need to determine the values of sine, cosine, tangent, cotangent, secant, and cosecant. Given that the point p=(3,-7) is on the terminal side of angle a, we can use the coordinates of the point to find the trigonometric functions.

First, we need to determine the values of the adjacent side and the hypotenuse. From the coordinates of point p, we have:

Adjacent side, x-coordinate = 3
Hypotenuse = distance between the origin and point p = sqrt((3)^2 + (-7)^2) = sqrt(9 + 49) = sqrt(58)

Now we can calculate the trigonometric functions:

• sin(a) = (opposite side) / (hypotenuse) = (-7) / sqrt(58)
• cos(a) = (adjacent side) / (hypotenuse) = 3 / sqrt(58)
• tan(a) = (opposite side) / (adjacent side) = (-7) / 3
• cot(a) = 1 / tan(a)
• sec(a) = 1 / cos(a)
• csc(a) = 1 / sin(a)