How do you use the point (3,6) on the terminal side of the angle to evaluate the six trigonometric functions?

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1 Answer
Nghi N
Jun 27, 2017

#tan x = y/x = 6/3 = 2#
#cos^2 x = 1/(1 + tan^2 x) = 1/(1 + 4) = 1/5#
#cos x = +- 1/sqrt5#
#sin^2 x = 1 - cos^2 x = 1 - 1/5 = 4/5#
#sin x = +- 2/sqrt5 = +- (2sqrt5)/5#
#cot x = 1/(tan) = 1/2#
#sec x = 1/(cos) = +- sqrt5#
#csc x = 1/(sin) = +- sqrt2/5#

Note. The reason we have 2 opposite values for sin x, and cos x, is
because there are 2 arcs (angles) that have the same tan value.
#x = 63^@43# and #x = 63.43 + 180 = 243^@43#

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