## Related Topics

- How to Evaluate Trigonometric Function
- How to Solve Angles and Angle Measure
- How to Solve Coterminal Angles and Reference Angles
- How to Find Missing Sides and Angles of a Right Triangle

## Step by step guide to solve Trig Ratios of General Angles

- Learn common trigonometric functions:

\(\theta\) | \(0^\circ\) | \(30^\circ\) | \(45^\circ\) | \(60^\circ\) | \(90^\circ\) |

\(sin\) \(\theta\) | \(0\) | \(\frac{1}{2} \) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) |

\(cos\) \(\theta\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | \(0\) |

\(tan\) \(\theta\) | \(0\) | \(\frac{\sqrt{3}}{3}\) | \(1\) | \(\sqrt{3}\) | Undefined |

### Trig Ratios of General Angles – Example 1:

Find the trigonometric function: \(cos\) \(120^\circ\)

**Solution**:

\(cos\) \(120^{\circ}\)

Use the following property: \(cos\)\((x)=\) \(sin\)\((90^{\circ}-x)\)

\(cos\) \(120^{\circ} =\) \(sin\) \(( 90^{\circ} -120^{\circ})=\) \(sin ( -30^{\circ}) \)

Now use the following property: \(sin (-x)\)\(=- sin (x)\)

Then: \(sin ( -30^{\circ})=-sin (30^{\circ}\))\(=-\frac{1}{2 }\)

### Trig Ratios of General Angles – Example 2:

Find the trigonometric function: \(sin\) \(135^\circ\)

**Solution**:

Use the following property: \(sin\)\((x)=\) \(cos\)\((90^\circ-x)\)

\(sin\) \(135^\circ=\) \(cos\)\((90^\circ-135^\circ)=\) \(cos\)\((-45^\circ)\)

Now use the following property: \(cos\)\((-x)=cos x\)

Then: \(cos\)\((-45^\circ)=\) \(cos\)\((45^\circ)=\frac{\sqrt{2}}{2 }\)

### Trig Ratios of General Angles – Example 3:

Find the trigonometric function: \(sin\) \(-120^\circ\)

**Solution**:

Use the following property: \(sin\)\((-x)=-\) \(sin\)\((x)\)

\(sin\)\(-120^\circ=-\) \(sin\) \(120^\circ\) , \(sin\)\(120^\circ=\frac{\sqrt{3}}{2}\)

Then: \(sin\)\(-120^\circ=-\frac{\sqrt{3}}{2}\)

### Trig Ratios of General Angles – Example 4:

Find the trigonometric function: \(cos\) \(150^\circ\)

**Solution**:

\(cos\) \(150^{\circ}\)

Use the following property: \(cos\)\((x)=\) \(sin\)\((90^{\circ}-x)\)

\(cos\) \(150^{\circ} =\) \(sin\) \(( 90^{\circ} -150^{\circ})=\) \(sin ( -60^{\circ}) \)

Now use the following property: \(sin (-x)\)\(=- sin (x)\)

Then: \(sin ( -60^{\circ})=-sin (60^{\circ}\))\(= -\frac{\sqrt{3}}{2}\)

## Exercises

### Use a calculator to find each. Round your answers to the nearest ten–thousandth.

- \(\color{blue}{sin \ – 120^\circ}\)
- \(\color{blue}{sin \ 150^\circ}\)
- \(\color{blue}{cos \ 315^\circ}\)
- \(\color{blue}{cos \ 180^\circ}\)
- \(\color{blue}{sin \ 120^\circ}\)
- \(\color{blue}{sin \ – 330^\circ }\)

### Download Trig Ratios of General Angles Worksheet

- \(\color{blue}{-\frac{\sqrt{3}}{2}}\)
- \(\color{blue}{\frac{1}{2}}\)
- \(\color{blue}{\frac{\sqrt{2}}{2}}\)
- \(\color{blue}{-1}\)
- \(\color{blue}{\frac{\sqrt{3}}{2}}\)
- \(\color{blue}{\frac{1}{2}}\)

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