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:
| \(\theta\) | \(0^\circ\) | \(30^\circ\) | \(45^\circ\) | \(60^\circ\) | \(90^\circ\) |
| 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 |
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.
- \(\color{blue}{sin \ – 120^\circ}\)
- \(\color{blue}{sin \ 150^\circ}\)
- \(\color{blue}{cos \ 315^\circ}\)
- \(\color{blue}{cos \ 180^\circ}\)
- \(\color{blue}{sin \ 120^\circ}\)
- \(\color{blue}{sin \ – 330^\circ }\)
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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