Honors Precalculus
Chapter 4
Flash cards
1. Convert from DMS to decimal form.
4830' 36''
3. Convert from DMS to radians.
120 
3π
5
π
3
9. Compass Bearing:
graph 210 
4. Convert from DMS to radians.
6. Convert from radians to degrees.
2
7. Use the appropriate arc length formula
to find the missing information.
r= ? θ =
21.2 
11.83
5. Convert from radians to degrees.
s=2.5 cm
2. Convert from decimal form to DMS.
8. A central angle θ intercepts arcs s1 & s2
on two concentric circles with radii r1 & r2
respectively. Find the missing info.
θ = ? r1 = 8 km s1 = 36 km r2 = ?
s2 = 72 km
10. Find the values of all 6 trig functions of
the angleθ .
11. Assume thatθ is an acute angle in a right triangle.
Evaluate the remaining trig functions.
sinθ =
12. Evaluate without using a calculator.
⎛π⎞
cos ⎜ ⎟
⎝ 4⎠
2
3
13. Evaluate without using a calculator.
14. Evaluate using a calculator.
⎛π⎞
sec ⎜ ⎟
⎝ 3⎠
15. Solve for side (a) .
Right triangle:
B = 57 ,b = 32
17. Point P is on the terminal side of angle θ .
Evaluate the 6 trig functions for θ . If the
function is undefined write undefined.
(−3,0 )
19. State the sign (+ or -) of a) sint b) cost
c) tant for values of t in the interval given.
⎛π ⎞
⎜⎝ ,π ⎟⎠
2
sec1.24
16. Solve for all of its unknown parts.
Right Triangle:
A = 20 ,a = 12.3
18. Point P is on the terminal side of angle θ .
Evaluate the 6 trig functions for θ . If the
function is undefined write undefined.
(5, −2)
20. Choose the point on the terminal side of θ .
θ=
2π
3
21.Evaluate
without using a calculator by using
ratios in a reference triangle.
22.Find
a) sinθ b) cosθ c) tan θ for the given angle.
tan 300
−270 
23. Evaluate without using a calculator.
1
Find cos θ and cot θ if sinθ = & tanθ < 0
4
24. Evaluate without using a calculator.
4
Find sec θ and csc θ if cot θ = − & cos θ < 0
3
25. Find the amplitude of the function and use
the language of transformations to describe
how the graph of the function is related ot y = sinx
y=
2
sin x
3
26. Find the period and use language of
transformations to describe how graph is
related to y = cos x
y = cos (−7 x )
28. Graph one period of the function. Be sure
to show the scale on both axes.
y = −.5 sinx
27. Find the period and use language of
transformations to describe how graph is
related to y = cos x
y=
1
2x
cos
4
3
29. Graph one period of the function. Be sure
to show the scale on both axes.
y = 5cos 2x
30.Describe
the transformations required to
obtain the graph.
y=
31. Construct a sinusoid with the given amplitude
and period that goes thru the given point.
3
x
sin
4
5
amplitude 1.5, period
32.State the amplitude, period, phase shift
and vertical translation.
y=
33. Describe the transformations required to
obtain the given function from a basic
trig graph.
7 ⎛
5⎞
sin ⎜ x + ⎟ − 1
3 ⎝
2⎠
34. Find the exact value.
y = 2 tanπ x − 2
35. Find the approximate value. Give answer in
degrees.
⎛ 1⎞
cos −1 ⎜ ⎟
⎝ 2⎠
36. Find the exact value without a calculator.
⎛
⎛ 1⎞ ⎞
cos ⎜ sin −1 ⎜ ⎟ ⎟
⎝ 2⎠ ⎠
⎝
38. Find the exact value without a calculator.
⎛ ⎛ π ⎞⎞
cos −1 ⎜ tan ⎜ − ⎟ ⎟
⎝ ⎝ 4 ⎠⎠
π
, point (1,0)
6
arccos(.67)
37. Find the exact value without a calculator.
(
sin 2 tan −1 ( −1)
)
39.Find the exact solution without a calculator.
sin−1 (sin x ) =
π
10
⎜⎝
⎜⎝
⎟
4 ⎠ ⎟⎠
40. Find an algebraic expression equivalent
to the given expression.
10
41. Find an algebraic expression equivalent
to the given expression.
sin (arccos 3x )
42. The angle of depression of a buoy from the top
of the Barnegat Bay light house 140 feet above
the surface of the water is 6 degrees. Find the
distance x from the base of the lighthouse to the buoy.
43. From the top of the 100 ft tall Altgelt Hall a man
observes a car moving toward the building. If
the angle of depression of the car changes from
22  to 46 during the period of observation, how
far does the car travel?
44. A large, helium-filled penguin is moored at the
beginning of a parade route awaiting the start of
the parade. Two cables attached to the underside
of the penguin make angles of 48 and 40 with
the ground and are in the same plane as a
perpendicular line from the penguin to the ground.
If the cables are attached to the ground 10 feet from
each other, how high above the ground is the penguin?
⎛
⎛ 2 ⎞⎞
cos ⎜ cot−1 ⎜ ⎟ ⎟
⎝ x⎠⎠
⎝