Solving Trig
Equations
Exact Values
C
AS
T
0o180o
270o
90o
180o - xo
180o + xo
xo
360o + xo CAST
diagram
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0 1 0
1 3 1
2 2 31 1
12 2
3 1 3
2 2
1 0
o
o
o
o
o
sin cos tan
0
30
45
60
90
ALWAYS work with 1st Quad
then translate
Solve: tanxo + 1 = 0
tanxo = -1
xo = tan-1 (1)
xo = 45o
Solution : xo = 180o - 45o = 135o
xo = 360o - 45o = 315o
Example
1
-1
090o 180o 270o 360o45o θ
Find x coordinates for A and B
A B0.4
sinxo = 0.4
xo = sin-1 (0.4)
xo = 23.6o
xo =180o - 23.6o = 156.4o
C
AS
T0o180o
270o
90o
C
AS
T0o180o
270o
90o
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Solving Trig Equations
Example 5 Type 4 :
Solving the equation cos2x = 1 in the range 0o to 360o
Graphically what are we
trying to solve
cos xo = ± 1
cos xo = 1
cos2 xo = 1
xo = 0o and 360o
C
AS
T0o180
o
270o
90o
cos xo = -1xo = 180o
