Multiple Solution Problems1) Solve Sin(2x) = 0.6

2) Solve Cos(2x) = 0.8

3) Solve 5Tan(2x) = 8.4

4) Solve Sin(2x + 15) = 0.85

5) Solve 0.5Cos(0.5x) + 4 = 3.92

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Multiple solutions A

180 0, 360A

T C

S

1) Solve Sin(2x) = 0.6

Let A = 2x Sin(A) = 0.6 A = Sin-1 0.6 = 36.9° and A = 180 – 36.9 = 143.1°

The next two solutions for A = 396.9° and A = 503.1°

So A = 36.9°, 143.1°, 396.9°, 503.1° x = A ÷ 2 so x = 18.5° and 71.7° and 198.5° and 251.6°2) Solve Cos(2x) = 0.8

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Multiple solutions B

4) Solve Sin(2x + 15) = 0.85

3) Solve 5Tan(2x) = 8.4

5) Solve 0.5Cos(0.5x) + 4 = 3.92

180 0, 360A

T C

S

180 0, 360A

T C

S

180 0, 360A

T C

S

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Overview: Trig EquationsHome

eg) Solve 5Sin(2πx) = 4

Sin(A) = 0.8

Sin(2πx) = 0.8

1) Rearrange the equation into the form Sin A =

Where A = 2πx2) Find a solution to the trig equation Check if degrees or radians!

Note π so use radians3) Find several solutions for ‘A’ Using graph or unit circle

A = π – 0.927 = 2.214 rad4) Use ‘A’ to find solutions for ‘x’

A = 0.927 or 2.214

x = 0.927 ÷ 2π = 0.148

x = 2.214 ÷ 2π = 0.352

A = Sin-1 0.8 = 0.927 radians

Use each ‘A’ to find ‘x’

1 2 3 4 5 – 1 – 2 – 3 – 4 – 5

y

x

0.5

0.5

1

1

1

1

2

2

3

3

4

4

5

5

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

– 5

– 5

Where A = 2πx so x = A ÷ 2π