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.

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

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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: \(cos\)\((x)=\) \(sin\)\((90^{\circ}-x)\)
\(cos\) \(120^{\circ} =\) \(sin\) \(( 90^{\circ} -120^{\circ})=\) \(sin ( -30^{\circ}) \)

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.

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

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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