SOLUTION: A point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-6,-5)
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Question 1159215: A point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-6,-5) Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the coordinate point of the angle is at (-6,-5).
tht means the x-value of the coordinate point is -6 and the y-value of the coordinate point is -5.
the hypotenuse of the triangle formed is equal to sqrt((-6)^2 + (-5)^2) which is equal to sqrt(36 + 25) = sqrt(61).
the side opposite the angle is the y-value = -5.
the side adjacent to the angle is the x-value = -6.
the hypotenuse of the triangle formed is equal to sqrt(61).
the hypotenuse of the triangle formed is always positive, regardless of what quadrant the angle is in.
the angle is in the third quadrant.
in the first quadrant the angle would be arctan(-5/-6) = 39.80557109.
in the third wuadrant, the equivalent angle would be 180 + that = 219.8055711.
you can use your calculator to confirm that the decimal equivalents of the trigonometric function are correct.
i did; they are confirmed to be accurate.
graphically, the angle and the trig function are as shown below, with the trig functions rounded to 3 decimal digits (the calculator does that automatically).
here's a couple of references that might help you to understand.
