Find the values of sin t cos t tan t csc t sec t and cot t i

Find the values of sin t, cos t, tan t csc t, sec t, and cot t if p = (- squareroot 91/10, - 3/10) is the point on the unit circle that corresponds to the real number t. sin t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) cos t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) tan t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) csc t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) sec t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) cot t = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

P=(-sqrt91/10,-3/10)

tan theta=y/x= -3/sqrt-91= 3sqrt91/91

Here adjacent=sqrt91    and   opposite=3

Therefore hypotenuse= sqrt(sqrt91²+3²)=10

sin theta=opposite/hypotenuse= -3/10

cos theta=adjacent/hypotenuse= -sqrt91/10

csc theta=1/sin theta=-10/3

sec theta=1/cos theta=-10/sqrt91= -10sqrt91/91

cot theta= 1/tan theta= sqrt91/3