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LESSON
7:Test
1. Convert each of the following to degree
measure.
3. An electric motor turns at 3600 rpm’s (rev’s
per minute). Express this angular
velocity in radians per second to the nearest hundredth.
5. Find the exact value of the following.
6. Sketch the graph
of the basic function 
Use transformations to sketch 
.
Find the amplitude, period, phase shift,
domain and range.
7. The graph below shows a sine function of the form y = a sin k(x – d) + c. find the values of the parameters a,k, d, c.
9. Prove the
following identities.
Solutions:
1. Convert each of the following to degree
measure.
3. An electric motor turns at 3600 rpm’s (rev’s
per minute). Express this angular
velocity in radians per second to the nearest hundredth.
Solution:
5. Find the exact value of the following.
Solution:
.
Find the amplitude, period, phase shift,
domain and range.
Solution: For 
,
construct a table of values of key points and plot the graph [blue]:
|
x0 |
0 |
90 |
180 |
270 |
360 |
|
y |
1 |
0 |
-1 |
0 |
1 |
(x, y) -----------------------à ( ½ x – 450,
- ½ y – 1)
Using
the mapping and the points from the table above we get points for the
transformed graph
(x, y) ------------------------------à( ½ x – 450,
- ½ y – 1)
(0,
1) -------------------------à (-450, -1.5)
(900, 0)
-----------------------à (00, -1 )
(1800, -1)
---------------------à (450, -0.5)
(2700 , 0)
---------------------à (900, -1)
(3600, 1)
----------------------à (1350, -1.5) [red graph
at left]
In radians, the points (see table
at top of page) would be:
Amplitude: |a| =
½
Domain of 1 period or cycle
(between red dots on graph):
Range: The maximum value of y is -0.5 and
the minimum value is –1.5
7. The graph below shows a sine function of the form y = a sin k(x – d) + c. find the values of the parameters a,k, d, c.
9. Prove the
following identities.
Proof:
Proof:
