Algebra II / Mr. Hansen

Name: _____________________________

5/5/2000 Practice Test on §§13-1 through 13-6
(corrected version)

 

Show all work unless the problem specifically says not to
For full credit, show all work. You are permitted to use memorized facts (e.g., sin 3p /2 = –1) without justification, but show all steps in computation.

Show exact values for the "salient points" on the unit circle
For example, do not give sin 3p /4 = 0.7071, since that is an approximation. An approximation would be acceptable for sin 7p /9, since that is not one of the salient points whose circular function values you are supposed to know.

Assume radian measure for all angles unless degrees are stated with a ° symbol
Any angle whose measure is not followed by a ° symbol is to be taken in radians. Similarly, anything angle whose measure you write as part of an answer will be assumed to be in radians unless you add the ° symbol.

Notation
You are expected to be familiar with the following notation and how to deal with the lack of certain buttons on your calculator. For example, there are no buttons for csc or csc–1.
sin q , csc q
cos q , sec q
tan q , cot q
sin–1 x, csc–1 x
cos–1 x, sec–1 x
tan–1 x, cot–1 x

Formula Bin
The following formula will be provided to you without explanation. In other words, you must know what A, B, C, and D mean.
y = C + A cos B(x – D)

Calculator-free zone
The first four questions are to be done without your calculator. On the real test, you would need to turn these problems in before taking out your calculator and working on the rest of the test.

1.

Draw a very large unit circle and mark all 16 of the salient points that we learned about. Show angle measure in both degrees and radians.

 
2.
On your unit circle in question 1, show the sine, cosine, and tangent of all the angles in the first and fourth quadrant.

 
3.
Using proper notation, mark the cosecant of any one angle in the second quadrant

 
4.
Using proper notation, mark the cotangent of any one angle in the third quadrant.

 
5.
Use your calculator to compute each of the following to 3 decimal places or to the nearest minute if you use degrees and minutes. No work is required.

 

(a)

cos 15° 14'

 

(b)

cot 12

 

(c)

csc–1 382

 
6.
In question 5, which one part can have an answer stated in either radians or degrees? ____ Now go ahead and give its answer in the other format. (If you originally gave radians, give the answer now in degrees and minutes, rounding to the nearest minute. If you originally gave degrees and minutes, give the answer now in radians.)

 
7.
Calculate each of the following using exact arithmetic. Your calculator is useful only as a double-check.

 

(a)

(sin p /2) (cos p /4) – (cot 2p /3)2

 

(b)

sin (sin–1 1/14) + tan–1 (tan 3p )

 
8.
Let x = time in days after Dec. 21, y = length of daylight observed at National Cathedral (in hrs.).

 

(a)

Is y = f (x) a periodic function? _____ Why or why not? ______________________

 

(b)

What is the period of f ?

 

(c)

Is f approximately sinusoidal?

 

(d)

State f (0) in words and with a numeric estimate.

 

(e)

State the values of A, B, C, and D. You may need to show some work.

 

 

 

 

 

 

 

(f)

Define the function f (x) and make a graph that indicates the features A, B, C, and D.

 
9.
Repeat question #8 with the following changes:
x = elapsed time (sec.)
y = height of a Coca-Cola can sitting on the seat of a 100-ft. ferris wheel as the wheel makes 4 complete revolutions per minute
Assume that the axle of the ferris wheel is 50 ft. off the ground, and the minimum height reached by the a seat is 3 ft.