SOLUTION: Determine the exact value of the six trigonometric functions given by the coordinates (-6,-1) Thank you!

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Question 1030505: Determine the exact value of the six trigonometric functions given by the coordinates (-6,-1)
Thank you!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the coordinate point if (-6,-1).
the triangle formed goes from the center (0,0) to this point.
the x-value is -6.
the y-value is -1.
the hypotenuse of this triangle is sqrt((-6)^2 + (-1)^2) = sqrt(37).

this is a right triangle where:
adjacent side is -6
opposite side is -1
hypotenuse is sqrt(37)

you can find all 6 of the trig functions as shown below:

sine = opp/hyp = -1/sqrt(37)

cosine = adj/hyp = -6/sqrt(37)

tangent = opp/adj = -1/-6 = 1/6

cosecant = 1/sine = -sqrt(37)/1

secant = 1/cosine = -sqrt(37)/6

cotangent = 1/tangent = 6/1

the diagram of your triangle is shown below.

figuring out what the angle is can get tricky unless you know a few tricks.

my trick is to assume the triangle is in the first quadrant.

i then get the angle in the first quadrant and, from there, i determine the angle in the quadrant that it is really in.

for example:

the angle is x in the diagram.

the sine of angle x is equal to opp/hyp = -1/sqrt(37).

i make that positive and i get sine of angle x is 1/sqrt(37).

i then go to the calculator and the calculator tells me that the angle is 9.462322208 degrees.

i then determine that the equivalent angle in the third quadrant is equal to 180 + 9.462322208 degrees = 189.462322208 degrees.

that's the equivalent angle in the third quadrant.

here's the diagram of the triangle formed by the coordinate point of (-6,-1).