Question

Let α be an angle, with 0 ≤ α < 2π. Given cos(2α) = 17/49 and 2α is in quadrant IV, find the exact values of the six trigonometric functions.

A) sin(α) = -4/7, cos(α) = -3/7, tan(α) = 4/3, cot(α) = 3/4, sec(α) = -7/3, csc(α) = -7/4
B) sin(α) = -4/7, cos(α) = 3/7, tan(α) = -4/3, cot(α) = -3/4, sec(α) = 7/3, csc(α) = -7/4
C) sin(α) = 4/7, cos(α) = -3/7, tan(α) = -4/3, cot(α) = 3/4, sec(α) = -7/3, csc(α) = 7/4
D) sin(α) = 4/7, cos(α) = 3/7, tan(α) = 4/3, cot(α) = -3/4, sec(α) = 7/3, csc(α) = 7/4

Answer 1

To find the values of the six trigonometric functions given cos(2α) = 17/49 and 2α is in quadrant IV, we can use the double-angle identity cos(2α) = 2cos^2(α) - 1 to find cos(α). Then, using the Pythagorean identity sin^2(α) + cos^2(α) = 1, we can find sin(α). From there, we can determine the values of the other trigonometric functions.

Step-by-step explanation:

To find the exact values of the trigonometric functions, we need to determine the values of sin(α), cos(α), tan(α), cot(α), sec(α), and csc(α) based on the given information.

Since cos(2α) = 17/49 and 2α is in quadrant IV, we can use the double-angle identity cos(2α) = 2cos^2(α) - 1 to solve for cos(α). Solving the equation, we get cos(α) = 3/7.

Using the Pythagorean identity sin^2(α) + cos^2(α) = 1, we can find sin(α). Substituting the value of cos(α), we get sin(α) = -4/7.

Using the definitions of the other trigonometric functions, we can find the values of tan(α), cot(α), sec(α), and csc(α) accordingly.