How to Solve Trig Ratios of General Angles

How to Solve 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

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⁡ \((-30^{\circ})=-\frac{1}{2 }\)

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\((-x)=cos⁡(x)\)
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:

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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