Beyond the Unit Circle

Question

Let  be the angle in standard position whose terminal side contains the point (1, 7). Find the values of the six trigonometric functions of .

Answer 1

tan(theta) = 7/1 = 7

cot(theta) = 1/7

7= opposite side, 1 = adjacent side

hypotenuse = sqr(49+1) = sqr50 = 5sqr2

sin(theta) = opposite side/hypotenuse = 7/5sqr2

csc(theta) = 1/sin(theta) = 5sqr2/7

cos(theta) = adjacent side/hypotenuse = 1/5sqr2

sec(theta) = 1/cos(theta) = 5sqr2/1 = 5sqr2