If theta is an acute angle of a right triangle and if cotang

If
theta
is an acute angle of a right triangle and if
cotangent theta equals square root of 5 ,
then find the values of the remaining five trigonometric functions for angle
theta.

Solution

cot theta=sqrt5

cot theta=adjacent/opposite

Therefore adjacent=sqrt5 and opposite=1

Hence hypotenuse=sqrt(5+1)=sqrt6

sin theta=opposite/hypotenuse

sin theta=1/sqrt6

cos theta=adjacent/hypotenuse=sqrt5/sqrt6

tan theta=1/cot theta=1/sqrt5

sec theta=1/cos theta=sqrt6/sqrt5

csc theta=1/sin theta=sqrt6