Solving Trig Equations

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