Download HW 6 - NDSU

MATH-105
Homework #6
Due Thursday 06/27/13
Name:
Make sure that you show all of your work and justify your answers for credit. Do
not use a calculator unless it is absolutely necessary. Simplify your answers
completely for full credit.
1. Find the exact values of the six trigonometric functions of the angle θ if the terminal side of θ contains
the given point (x, y) which is r units from the origin. Sketch two possible angles, one positive and one
negative, that satisfy the conditions on θ.
(a) (x, y) = (−3, 4)
(b) (x, y) = (−5, 12)
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MATH-105
Homework #6
Due Thursday 06/27/13
2. Use the known values on the unit circle to determine the following values. Be sure to draw a picture
and explain how you arrived at your answer.
(a) sin(225◦ )
(b) cot(330◦ )
(c) csc(300◦ )
3. Use a calculator to find the approximate values of the six trigonometric functions of θ.
(a) θ = −380◦
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MATH-105
Homework #6
Due Thursday 06/27/13
(b) θ = 1.3
(c) θ = 417◦
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MATH-105
Homework #6
Due Thursday 06/27/13
4. A downhill ramp of length 185 feet from a service drive to a highway has a −4.5◦ grade. Round all
answers to two decimal places.
(a) Sketch a model of the situation in a Cartesian system so that the ramp’s entry point S is at the
origin and the point W where th ramp meets the highway is in quadrant IV.
(b) Use the model in part (a) to find the location W of where the ramp meets the highway. Find the
elevation of the service drive above the highway and the horizontal distance spanned by the ramp.
(c) Find the slope of the ramp.
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MATH-105
Homework #6
Due Thursday 06/27/13
5. Suppose that θ is the radian measure of an angle in standard position. For each of the following, assume
that the terminal side of the angle lies in the stated quadrant along the given line. FInd the values of
the six trigonometric functions of θ.
(a) Quadrant III, line with equation y = 5x
(b) Quadrant IV, line with equation 12x + 4y = 0
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