The point #(-5,-2)# is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

1 Answer
Jan 27, 2018

Answer:

#sintheta~~-0.37#
#costheta~~-0.93#
#tantheta~~0.40#
#csctheta~~-2.69#
#sectheta~~-1.08#
#cottheta~~2.50#

Explanation:

Here's a diagram I made using Desmos:

enter image source here

The unknown angle #theta# can be calculated by using #tan# of the lengths we already know:

#theta = 180º + tan^-1(2/5)#

#~~180º+21.8º=201.8º#

You can use a calculator or a sine table to calculate the trig functions:

#sintheta~~-0.37#
#costheta~~-0.93#
#tantheta~~0.40#
#csctheta~~-2.69#
#sectheta~~-1.08#
#cottheta~~2.50#

If your calculator doesn't support #tan#, #csc#, #sec#, or #cot#, here are some helpful conversions you can use:

#tantheta=sintheta/costheta#

#csctheta=1/sintheta#

#sectheta=1/costheta#

#cottheta=1/tantheta=1/(sintheta/costheta)=costheta/sintheta#