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.

Answer 1

To find the trigonometric functions of angle a given that p=(3,-7) is a point on the terminal side of the angle, we can use the properties of right triangles. The six trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent. Using the given point p=(3,-7), we can calculate the values of these trigonometric functions.

Step-by-step explanation:

To find the trigonometric functions of angle a given that p=(3,-7) is a point on the terminal side of the angle, we can use the properties of right triangles. We can construct a right triangle with the hypotenuse as the line segment from the origin to the point p, the adjacent side as the x-coordinate of p, and the opposite side as the y-coordinate of p.

The six trigonometric functions are:

1. Sine (sin a): The ratio of the opposite side to the hypotenuse: sin a = y-coordinate of p / hypotenuse
2. Cosine (cos a): The ratio of the adjacent side to the hypotenuse: cos a = x-coordinate of p / hypotenuse
3. Tangent (tan a): The ratio of the opposite side to the adjacent side: tan a = y-coordinate of p / x-coordinate of p
4. Cosecant (csc a): The reciprocal of the sine: csc a = 1 / sin a
5. Secant (sec a): The reciprocal of the cosine: sec a = 1 / cos a
6. Cotangent (cot a): The reciprocal of the tangent: cot a = 1 / tan a

Using the given point p=(3,-7), we can calculate the values of these trigonometric functions.