Transcript SOLVING TRIG EQUATIONS

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SOLVING TRIG EQUATIONS
Multiple Angles
WJEC C2 January 2008
First step is to adjust the interval to be consistent with the Angle (3x+15)
0  x  180
15  3x  15  555
Next step is to find the INVERSE SIN of 0.5. This is sometimes called ARCSIN
And is written
Note that this is not a solution
sin 1 0.5  30
But is the PRINCIPAL VALUE
of 3x+15.
The PRINCIPAL VALUE is the Angle which is in the FIRST QUADRANT
That means the Angle which is between 0 and 90 degrees.
NOW use the CAST diagram
(or you can use the Graph of sin A)
to identify the other solutions for 3x+15
90
0  x  180
S
180
15  3x  15  555
A
30
30
30
30
C
T
270
Now we solve for x
3x  15  30
0
3x  15  150
Don’t forget we are looking for
solutions for 3x+15 up to 555 degrees!
3x  15  390
3x  15  510
3 x  15  30
3 x  30  15
3 x  15
15
x
3
x5
3x  15  150
3x  150  15
3x  135
135
x
3
x  45
3x  15  390
3x  390  15
3x  375
375
x
3
x  125
3x  15  510
3x  510  15
3x  495
495
x
3
x  165
FINAL SOLUTIONS
x  5 , 45 ,125 ,165