Suppose that θ is an acute angle and that cos θ = 9/√97. Use a right triangle to find all the other trigonometric functions of θ.

Question

sin0=?

tan0=?

sec0=?

cot0=?

csc0=?

Answer 1

cosx =9/sqr97

secx = sqr97/9

sinx = 4/sqr97

cscx = sqr97/4

tanx = 4/9

cotx = 9/4

opposite side, o, of the right triangle is sqr(97-9^2) =sqr16 = 4

cosx= adjacent side over hypotenuse = a/h

sinx =o/h

secx= h/a

cscx =h/o

tanx =o/a

cotx = a/o

Answer 2

cos(theta)=9/sqrt(97)

arccos(cos(theta))=arccos(9/sqrt(97))

theta=arccos(9/sqrt(97))

theta = 0.418 radian or 23.96 degree

now that you know the value for theta, use your favorite electronic device( ex. TI-83 calculator) to find the values for the 6 trig function