Ajay S. answered • 04/16/20
Precalculus Expert with Tutoring Results
Sure thing.
(a) sin(α) and cos(β)
Sine is equal to the opposite side over the hypotenuse in a right triangle. The opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7
Cos is equal to the adjacent side over the hypotenuse in a right triangle. The adjacent side to β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7
(b) tan(α) and cot(β)
Tan is equal to the opposite side over the adjacent in a right triangle. The opposite side to α is 4, but the adjacent side is unknown. Using the pythagorean theorem, we take the square root of 49-16 to get √33. Thus, tan(α) = 4/√33
Cot is equal to the adjacent side over the opposite in a right triangle (same thing as reciporcal of tangent). The adjacent side to β is 4 while the opposite is √33. This is equal to the 4/√33 as our final answer.
(c) sec(α) and csc(β)
Sec is equal to one divided by cosine, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33. Thus, our final answer is 7/√33.
Csc is equal to one divided by sine, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33. Thus, our final answer is 7/√33.
