Question

Determine the values of the six trigonometric functions for the angle θ, considering a = 3, b = 4, c = 5. What are the values?

a) sin(θ) = 3/5, cos(θ) = 4/5, tan(θ) = 3/4, csc(θ) = 5/3, sec(θ) = 5/4, cot(θ) = 4/3
b) sin(θ) = 4/5, cos(θ) = 3/5, tan(θ) = 4/3, csc(θ) = 5/4, sec(θ) = 5/3, cot(θ) = 3/4
c) sin(θ) = 3/5, cos(θ) = 4/5, tan(θ) = 4/3, csc(θ) = 5/3, sec(θ) = 5/4, cot(θ) = 3/4
d) sin(θ) = 4/5, cos(θ) = 3/5, tan(θ) = 3/4, csc(θ) = 5/3, sec(θ) = 5/4, cot(θ) = 4/3

Answer 1

Using the definitions of trigonometric functions for right triangles, the values of the six trigonometric functions for angle θ, given sides a = 3, b = 4, c = 5, are sin(θ) = 3/5, cos(θ) = 4/5, tan(θ) = 3/4, csc(θ) = 5/3, sec(θ) = 5/4, cot(θ) = 4/3.

Step-by-step explanation:

To determine the values of the six trigonometric functions for the angle θ given sides a = 3, b = 4, and c = 5, we can use the definitions of trigonometric functions for a right triangle. Assuming that side 'a' is the opposite side, 'b' is the adjacent side, and 'c' is the hypotenuse (recognizing the 3-4-5 Pythagorean triple indicates a right triangle), the functions are defined as follows:

• sin(θ) = opposite/hypotenuse = 3/5,
• cos(θ) = adjacent/hypotenuse = 4/5,
• tan(θ) = opposite/adjacent = 3/4,
• csc(θ) = 1/sin(θ) = 5/3,
• sec(θ) = 1/cos(θ) = 5/4,
• cot(θ) = 1/tan(θ) = 4/3.

So the correct values of the trigonometric functions for angle θ are:

• sin(θ) = 3/5,
• cos(θ) = 4/5,
• tan(θ) = 3/4,
• csc(θ) = 5/3,
• sec(θ) = 5/4,
• cot(θ) = 4/3.