A surveyor determines that the angle of elevation of a ...



MIFE 129 Test 5 11/26/08 Name___________________________ PART I _____/60

This part must be done without a calculator. Show all work.

1.Sketch the angle. Find the exact value of the trig function. (e.g. cos 90o = 0 ) (2 pts each)

i) [pic] ii) [pic] iii) [pic]

iv) [pic] v) [pic] vi) [pic]

2. Refer to the right triangle.

sin A = __________ csc A = __________ 15

cos A = __________ sec A = __________

(1 pt each)

tan A = __________ cot A = __________

3. i) Find all solutions of [pic] where [pic]. (12 pts)

ii) Find all solutions of [pic].

4. If sec t = -6/5 and tan t < 0, then:

(2 pts each)

i) t is in Quadrant _________

ii) cos t = _______

iii) [pic] = _______

iv) csc t = _________

v) [pic]= _______ (Think quadrants on unit circle.)

vi) [pic] = ______ (Think complementary angles in a triangle.)

5. i) [pic] (2 pts each)

ii) [pic] =

iii) [pic] =

iv) [pic]=

v) [pic]=

6. Give the amplitude, period, & phase shift of [pic]. Sketch the graph. Plot specific points. Label units.

(8 pts)

MIFE 129 Test 5 11/26/08 Name___________________________ PART II ______/40

You may use a calculator on this part. If the calculator was used, write the expression that you keyed in. When recording final answer give angles to two decimal places.

7. Solve the triangle if a = 15 and [pic]. Use radian measure. (5 pts)

A = ________ C = _________ B = __________

c = ________ b = __________

8. i) Convert 110o to radians. ________ ii) Convert 4 radians to degrees. _________ (2 pts)

9. The terminal side of an angle of t radians in standard position goes through the point[pic]. Find the exact values. (2 pts each)

i) [pic]= _______

ii) [pic]= _______

iii) [pic]= _______

10. Include labeled sketches in your solutions.

i) Your football has landed on your neighbor’s roof. When you are 25 feet from the building, the angle of elevation to the football is 21o. How high off the ground is your football? (7 pts.)

ii) The sonar of a navy cruiser detects a submarine 4000 feet from the cruiser. The angle between the waterline and the submarine is 34o. How deep is the submarine? (7 pts.)

11. Simplify [pic] (5 pts.)

12. Prove the following identities. (4 pts each)

i) [pic]

ii) [pic]

Math 129 Test 5 Problem Session

I. Sketch the angle. Evaluate the function at the given angle. (e.g. cos 90o = 0 )

i) cos [pic] tan [pic] sin 150o sec[pic]

ii) [pic] sin [pic] [pic] tan 60o

iii) sin [pic] [pic] sin[pic] cos 360o

II. Find sin t, cos t, and tan t if the terminal side of angle t in standard position passes through

i) (4, -3) ii) (-4, -3) iii) (-4, 3) (Hint: sketch the angle!)

III. i) Solve the right triangle given that [pic] and [pic]and the right angle is C.

ii) Given tan A = 3 and c = 12 and B is the right angle. Solve the right triangle.

iii) Given b = 25” and c = 8” and B is the right angle. Solve the right triangle.

IV. If cos t = -.3 and ( < t < 3(/2, find

a) sin t = b) sin (2π −τ) c) cos (t+ 4π) =

d) cot t = e) cot (t + 3π) ’ f) csc t =

V. Give the amplitude, period, & phase shift. Sketch the graph. Plot specific points. Label units.

i) [pic] ii)[pic] iii) [pic]

VI. Find the exact functional value.

i) [pic] ii) [pic] iii) [pic] iv) sin[cos-1(3/5)]

VII. Write as an algebraic expression in x.

i) sec(arctan 5x) ii) tan ( arcos 2x) iii) cot(arctan 3x)

Math 129 11/15/06 Name___________________________

Upper case variables refer to angles; lower case variables refer to lengths of sides.

The figures are not drawn to scale, but are to only give relative position of variables.

17

1. Given the triangle, find the following. 8

A

sin A = __________ csc A = __________ 15

cos A = __________ sec A = __________

tan A = __________ cot A = __________

2. Given sec A = 2 and b = 8.

c = ________

a = _________

A = ________

3. Solve the triangle if c = 5 and A = 60( .

C = _______ a = ________ b = __________

MIFE 117 / 129 11/24/08 Name_______________________________

1. Sketch the angle. Evaluate the function at the given angle. (e.g..cos 90o = 0 )

i) cos [pic] tan [pic] sin 150o sec[pic]

ii) [pic] sin [pic] [pic] tan 60o

iii) sin [pic] [pic] sin[pic] cos 360o

2. Give the amplitude, period of [pic]. Sketch at least 2 periods of the graph.

3. Give the amplitude, period, & phase shift of [pic]. Sketch at least 2 periods of the graph.

-----------------------

C

a b

B c A

Amplitude _______

Period __________

Phase Shift ______

C

a= 4 b

B c = 5 A

Amplitude _______

Period __________

Phase Shift ______

Amplitude _______

Period __________

C

a b

B c A

C

a b

B c A

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