# Trig Ratios of General Angles

Learn trigonometric ratios of general angles and how to solve math problems related to trig ratios by the following step-by-step guide.

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

• Learn common trigonometric functions:

### 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⁡ $$(-30^{\circ})=-\frac{1}{2 }$$

### 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$$(-x)=cos⁡(x)$$
cos$$(-45^\circ)=$$ cos$$(45^\circ)=\frac{\sqrt{2}}{2 }$$

### 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$$-120^\circ=-\frac{\sqrt{3}}{2}$$

### Example 4:

Find the trigonometric function: cos $$150^\circ$$

Solution:

Recall that cos $$150^\circ=-$$ cos $$30^\circ$$. Then: cos $$150^\circ=-$$ cos $$30^\circ=-\frac{\sqrt{3}}{2}$$

## Exercises

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

• $$\color{blue}{sin \ – 120^\circ}$$
• $$\color{blue}{sin \ 150^\circ}$$
• $$\color{blue}{cos \ 315^\circ}$$
• $$\color{blue}{cos \ 180^\circ}$$
• $$\color{blue}{sin \ 120^\circ}$$
• $$\color{blue}{sin \ – 330^\circ }$$

• $$\color{blue}{-\frac{\sqrt{3}}{2}}$$
• $$\color{blue}{\frac{1}{2}}$$
• $$\color{blue}{-\frac{\sqrt{2}}{2}}$$
• $$\color{blue}{-1}$$
• $$\color{blue}{\frac{\sqrt{3}}{2}}$$
• $$\color{blue}{\frac{1}{2}}$$

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