1 tan e cot d tb Solutiona tan thetayx 1sqrt 2 opposite 1

Solution

a. tan theta=y/x = - 1/sqrt 2

opposite= 1, adjacent =sqrt2

hypotenuse= sqrt(2+1)=sqrt3

sin theta= opposite/hypotenuse= 1/sqrt3

cos theta=adjacent/hypotenuse=-sqrt(2/3)

csc theta=1/sin theta= sqrt 3

sec theta=1/cos thet=-sqrt(3)/2

cot theta=1/tan theta=-sqrt2

b. tan theta=y/x=-1/5

opposite=1, adjacent=5

hypotenuse=sqrt(25+1)=sqrt26

sin theta=opposite/hypotenuse=-1/sqrt 26

cos theta=adjacent/hypotenyse= 5/sqrt 26

csc theta=1/sin theta=-sqrt 26

sec theta=1/cos theta= sqrt 26/5

cot theta=1/tan theta=-5