48 Suppose that 6 is an acute angle of a right triangle and

48. Suppose that 6 is an acute angle of a right triangle and sec (0) ind the six trigonometric functions of 0.

Solution

sec theta = 5/2

cos theta = 1 / sec theta = 2 / 5

cos theta = base / hypotenuse  

base = 2 , hypotenuse = 5

therefore, perpendicular = sqrt (5^2 - 2^2 ) { by pythagorean theorem }

perpendicular = sqrt 21

sin theta = perpendicular / hypotenuse = sqrt 21 / 5

cosec theta = 1 / sin theta = 5 / sqrt 21 = 5 sqrt 21 / 21

tan theta = perpendicular / base = sqrt 21 / 2

cot theta = 1 / tan theta = 2 / sqrt 21 = 2 sqrt 21/ 21