This is subscribed by bullcleo1, and presented by James Sousa:)
In subtopic 5.4-Solve the Trigonometric Function, the only aim is to FIND X.
-The question can be quite direct, for example:
1. Solve cos x-1=0, xε[0,2π]
Answer:
cos x=1
x=cos-1(1)
(scientific calculator time...)
x in quadrant 1=0
x in quadrant 4=2π-0
= 2π
Thus, x=0 and 2π Note: x cannot be more than 2π.
-The question can be a bit more complicated, for example:
2. Solve 3csc2 x-4=0 , xε[0,2π]
Answer:
3(1/cos2x)=4
(3/cos2x)=4
(cos2x/3)=1/4
cos2x=3/4
cos x= +/- √3/2
when cos x= +√3/2 When cos x=-√3/2
x in quadrant 1=π/6 x in quadrant 2=π-π/6
x in quadrant 4=2π-π/6 = 5π/6
= 11π/6 x in quadrant 3=π+π/6
= 7π/6
Thus, x = π/6, 11π/6, 5π/6 and 7π/6
The focus in subtopic 5.5 is on determining the instantaneous rate of change. It can be determined by finding the tangent through graphing calculator.
Normally a table will be given in the question, for exp:
Time(s)
|
Volume of air(mL)
|
0.0
|
131
|
0.5
|
134
|
1.0
|
141
|
1.5
|
152
|
2.0
|
167
|
2.5
|
153
|
3.0
|
129
|
and the common questions are:
a) make a scatter plot
-which can be solved by key in the data into gc and get the graph
steps: STAT, 1, key in the data, 2nd, STAT PLOT(on the plot),
Zoom 9, STAT; Move the cursor to CALC;C, Move cursor
to RegEQ, Var, Y-vars, 1, Enter, Move cursor Calculate,
Enter, (equation out), Graph. and....DONE! :D
b) determine the equation
-which can be determined from gc too after getting the graph
c) the instantaneous rate of change at x.
-can be determined from the tangent, by using gc.
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