The point (4,3) 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?

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Answer 1 · 2017-09-12T17:03:02

Sine #= 3/5 = 0.6#
Cosine #= 4/5 = 0.8#
Tangent #=3/4 = .75#
Cotangent =#4/3 = 1.33#
Secant #=5/4 = 1.25#
Cosecant #=5/3 = 1.67#

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Begin by drawing the terminal side in standard position and drawing the associated triangle.

Using the Pythagorean Theorem calculate the missing side the hypotenuse. (This is a Pythagorean Triplet 3-4-5)

We now have a triangle with values of

#x = 4#
#y = 3#
#h = 5#

The six trigonometric functions include

Sine #= y/h#
Cosine #= x/h#
Tangent #y/x#
Cotangent =#x/y#
Secant #=h/x#
Cosecant #=h/y#

Sine #= 3/5 = 0.6#
Cosine #= 4/5 = 0.8#
Tangent #= 3/4 = .75#
Cotangent =#4/3 = 1.33#
Secant #=5/4 = 1.25#
Cosecant #=5/3 = 1.67#