Solving Trig Equations 1 - Mathematical Association



Solving Trig Equations 1

[pic]

Solve the following trig equations giving angles in the range [pic] to 1 decimal place

|Equation |Principal Value |Other Quadrant |Cast Diagram |All solutions in the range |

| |(value from calculator) | | | |

| | | |[pic] | |

|Example: |[pic] |3rd | |[pic] |

|[pic] | | | | |

|1. [pic] | | | | |

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|2. [pic] | | | | |

| | | | | |

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|3. [pic] | | | | |

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|4. [pic] | | | | |

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|5. [pic] | | | | |

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| | | | | |

Solving Trig Equations 2

[pic]

Solve the following trig equations giving angles in the range [pic]

|Equation |Principal Value |Other Quadrant |Cast Diagram |All solutions in the range |

| |(value from calculator) | | | |

|Example: | | |[pic] | |

|[pic][pic] |[pic] |3rd | |[pic] |

|1. [pic] | | | | |

| | | | | |

| | | | | |

|2. [pic] | | | | |

| | | | | |

| | | | | |

|3. [pic] | | | | |

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|4. [pic] | | | | |

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|5. [pic] | | | | |

| | | | | |

| | | | | |

Solving Trig Equations 3

Solve the following trig equations giving angles in the range [pic], giving your answers to one decimal place

|Equation |Working out |Principal Value(s) |Cast Diagram (or diagrams) |All solutions in the range |

| | |(from calculator) | | |

|Example |[pic] |[pic] |[pic] |[pic] |

|[pic] | | | | |

|1. [pic] | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|2. | | | | |

|[pic] | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|3. | | | | |

|[pic] | | | | |

|(For this one you will need to | | | | |

|do the stages in a different | | | | |

|order: principal value first, | | | | |

|then cast diagram, then working| | | | |

|out) | | | | |

Solving Trig Equations 4

Solve the following trig equations giving angles in the range [pic], giving your answers to 2 decimal places

|Equation |Working Out |Principal Value(s) |Cast Diagram (or diagrams) |All solutions in the range |

|Example |[pic] | |[pic] | |

| | |[pic] | |[pic] |

|[pic] | | | | |

|1. | | | | |

|[pic] | | | | |

| | | | | |

| | | | | |

| | | | | |

|2. | | | | |

|[pic] | | | | |

| | | | | |

| | | | | |

| | | | | |

| | | | | |

|3. | | | | |

|[pic] | | | | |

|(Remember to do the stages in a | | | | |

|different order for this one.) | | | | |

| | | | | |

|4. | | | | |

|[pic] | | | | |

| | | | | |

| | | | | |

| | | | | |

Trig Equations Extension A

Solve the following trig equations for the range given:

|Question |Working out |Solution |

|1. | | |

|[pic] | | |

|2. | | |

|[pic] | | |

|3. | | |

|[pic] | | |

|4. | | |

|[pic] | | |

|5. | | |

|[pic] | | |

|6. | | |

|[pic] | | |

|7. | | |

|[pic] | | |

|8. | | |

|[pic] | | |

|9. | | |

|[pic] | | |

|10. | | |

|[pic] | | |

Trig Equations Extension B

Solve the following trig equations for the range given:

|Question |Working out |Solution |

|1. | | |

|[pic] | | |

|2. | | |

|[pic] | | |

|3. | | |

|[pic] | | |

|4. | | |

|[pic] | | |

|5. | | |

|[pic] | | |

| | | |

| | | |

|6. | | |

|[pic] | | |

| | | |

|7. | | |

|[pic] | | |

| | | |

|8. | | |

|[pic] | | |

| | | |

| | | |

Solutions to Trig Equation Sheets: 1, 2 and Extension A

Sheet 1:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

Sheet 2:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

Extension A:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

Solutions to Trig Equation Sheets: 3, 4 and Extension B

Sheet 3:

1. [pic]

2. [pic]

3. [pic]

Sheet 4:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

Extension B:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

-----------------------

All

1st

Cosine

4th

Sine

2nd

Tan

3rd

T

S

A

C

[pic]

[pic]

0

[pic]

1.11

1.11

17.5

17.5

The cast diagram shows you the quadrants in which the named trig functions are positive. In the example below we want the quadrants where sine is negative. Sine is positive in the 1st and 2nd quadrants, so it must be negative in the 3rd and 4th quadrants.

[pic]

[pic]

[pic]

[pic]

19.5

30

0.93

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