Use the given value of a trigonometric function of to find the values of the other five trigonmetric functions. Assume is an acute angle.

Question

Use the given value of a trigonometric function of to find the values of the other five trigonmetric functions. Assume is an acute angle.

CSC = 2

Answer 1

cscx=2 = hypotenuse/opposite side

It's a 2-1-sqr3 right triangle third side = sqr(2^2-1^2 = sqr(4-1)=sqr3 = adjacent side

sinx=1/cscx = 1/2

cosx = adjacent side/hypotenuse sqr3/2

secx = 1/cosx = 2/sqr3 = (2/3)sqr3

tanx = sinx/cosx = 1/2 over sqr3/2 = 1/sqr3 = sqr3/3

cotx = 1/tanx = sqr3

x = 30 degrees = pi/6 radians