Final answer:
The values of the six trigonometric functions, cos, sin, tan, csc, sec, and cot, can be found for = 45° and = 315° when cos(2°) = 1/√2.
Step-by-step explanation:
Given the equation cos(2°) = 1/√2, we can solve for by taking the inverse cosine of both sides. Since cos is positive in the first and fourth quadrants, we have two possible values for : = 45° and = 315°.
To find the values of the six trigonometric functions, we can use the unit circle or trigonometric identities. The values for = 45° are:
- cos(45°) = √2/2
- sin(45°) = √2/2
- tan(45°) = 1
- csc(45°) = √2
- sec(45°) = √2
- cot(45°) = 1
The values for = 315° can be found by considering the symmetry of the unit circle, where cos and sin have the same absolute value but opposite signs in the fourth quadrant. Therefore, the values are:
- cos(315°) = -√2/2
- sin(315°) = -√2/2
- tan(315°) = 1
- csc(315°) = -√2
- sec(315°) = -√2
- cot(315°) = 1