Trig Ratios of General Angles

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