The point (-1,1) 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?

Question

20794 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-25T17:24:12

See answers below

Given: terminal side point #(-1,1)#

The point #(-1, 1)# is in the 2nd quadrant.

It has the #x# value #= -1# and the #y#-value #= 1#. Drop the point to the #x#-axis and form a reference triangle.

Using the Pythagorean Theorem #r = sqrt((-1)^2 + 1^2) = sqrt(2)#

#sin theta = y/r = 1/sqrt(2) = 1/sqrt(2) * sqrt(2)/sqrt(2) = sqrt(2)/2#

#cos theta = x/r = -1/sqrt(2) = -1/sqrt(2) * sqrt(2)/sqrt(2) = -sqrt(2)/2#

#tan theta = y/x = 1/-1 = -1#

#csc theta = 1/(sin theta) = r/y = sqrt(2)/1 = sqrt(2)#

#sec theta = 1/(cos theta) = r/x = sqrt(2)/-1 = -sqrt(2)#

#cot theta = 1/(tan theta) = x/y = -1/1 = -1#