SOLUTION: what are the exact values of the six trigonmetric functions for the following angle 300 degrees? sin 300= cos 300= tan 300= cot 300= sec 300= csc 300=

Algebra ->  Trigonometry-basics -> SOLUTION: what are the exact values of the six trigonmetric functions for the following angle 300 degrees? sin 300= cos 300= tan 300= cot 300= sec 300= csc 300=      Log On


   

Question 563845: what are the exact values of the six trigonmetric functions for the following angle 300 degrees?
sin 300=
cos 300=
tan 300=
cot 300=
sec 300=
csc 300=
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
300 degrees is in the fourth quadrant.
the equivalent angle in the first quadrant would be 360 - 300 = 60 degrees.
this is a common angle that you can find the exact trigonometric functions for.
they are:
sin(60) = sqrt(3)/2
cos(60) = 1/2
tan(60) = sqrt(3)
cot(60) = sqrt(3)/3
sec(60) = 2
csc(60) = 2*sqrt(3)/3
that's the equivalent angle in the first quadrant where all trigonometric functions are positive.
when the angle is in the fourth quadrant, the signs of the trigonometric functions are as follows:
sine = negative
cosine = positive
tangent = negative
cotangent = negative
secant = positive
cosecant = negative
based on that, then:
sin(300) = - sqrt(3)/2
cos(300) = + 1/2
tan(300) = - sqrt(3)
cot(300) = - sqrt(3)/3
sec(300) = + 2
csc(300) = - 2*sqrt(3)/3
note that:
cotangent = 1 / tangent
secant = 1 / cosine
cosecant = 1 / sine