Final answer:
To find the values of the six trigonometric functions for angle A, we need to find the ratios of the sides of the triangle formed by the point (16, 30), the x-axis, and the hypotenuse.
Step-by-step explanation:
To find the values of the six trigonometric functions for angle A, we need to find the ratios of the sides of the triangle formed by the point (16, 30), the x-axis, and the hypotenuse. Since the point lies on the terminal side of angle A, we can use the x-coordinate (16) as the adjacent side and the y-coordinate (30) as the opposite side. The hypotenuse can be found using the Pythagorean theorem: hypotenuse = sqrt(adjacent^2 + opposite^2).
Once we have the values of the adjacent, opposite, and hypotenuse, we can calculate the six trigonometric functions:
- Sine (sin A) = opposite / hypotenuse
- Cosine (cos A) = adjacent / hypotenuse
- Tangent (tan A) = opposite / adjacent
- Cosecant (csc A) = 1 / sin A
- Secant (sec A) = 1 / cos A
- Cotangent (cot A) = 1 / tan A
Substituting the values, we get the six trigonometric functions for angle A.