Solving Trig Equations

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Solving Trig Equations Exact Values C A S T 0 o 180 o 270 o 90 o 180 o - x o 180 o + x o x o 360 o + x o CAST diagram undefined 0 1 0 1 3 1 2 2 3 1 1 1 2 2 3 1 3 2 2 1 0 o o o o o sin cos tan 0 30 45 60 90 ALWAYS work with 1 st Quad then translate olve: tanx o + 1 = 0 tanx o = -1 x o = tan -1 (1) x o = 45 o Solution : x o = 180 o - 45 o = 135 o x o = 360 o - 45 o = 315 o Exampl e 1 -1 0 90 o 180 o 270 o 360 o 45 o θ Find x coordinates for A and B A B 0.4 sinx o = 0.4 x o = sin -1 (0.4) x o = 23.6 o x o =180 o - 23.6 o = 156.4 o C A S T 0 o 180 o 270 o 90 o C A S T 0 o 180 o 270 o 90 o

description

ALWAYS work with 1 st Quad then translate. 90 o. S. A. 0 o. 180 o. C. T. 270 o. 180 o - x o. x o. 180 o + x o. 360 o + x o. CAST diagram. Exact Values. Solving Trig Equations. Example. B. A. 0.4. Solve: tanx o + 1 = 0 . θ. tanx o = -1 . x o = tan -1 (1) . - PowerPoint PPT Presentation

Transcript of Solving Trig Equations

Page 1: 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

Page 2: Solving Trig Equations

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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