# How to Solve Trig Ratios of General Angles? (+FREE Worksheet!)

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:

### 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.

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

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

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