How to Evaluate Trigonometric Function? (+FREE Worksheet!)

Learn how to evaluate trigonometric functions in a few simple steps with examples and detailed solutions.

How to Evaluate Trigonometric Function? (+FREE Worksheet!)

Related Topics

Step by step guide to Evaluating Trigonometric Function

  • Find the reference angle. (It is the smallest angle that you can make from the terminal side of an angle with the \(x\)-axis.)
  • Find the trigonometric function of the reference angle.

Evaluating Trigonometric Function – Example 1:

Find the exact value of trigonometric function. \(tan\)\(\frac{4π}{3}\)

Solution:

Rewrite the angles for an \(\frac{4π}{3} \):
\(tan\) \(\frac{4π}{3}=tan \frac{3π+π}{3}=tan⁡(π+\frac{1}{3} π) \)
Use the periodicity of \(tan\): \(tan\)\((x+π .k)= tan (x)\)
\(tan\)\(⁡(π+\frac{1}{3} π)=\) \(tan\)\(⁡(\frac{1}{3} π)=\sqrt{3} \)

Evaluating Trigonometric Function – Example 2:

Find the exact value of trigonometric function. \(cos\) \(270^\circ\)

Solution:

Write \(cos\) \((270^\circ)\) as \(cos\) \((180^\circ+90^\circ)\). Recall that \(cos⁡180^\circ=-1,cos ⁡90^\circ =0\)
The reference angle of \(270^\circ\) is \(90^\circ\). Therefore, \(cos\) \(270^\circ=0\)

Evaluating Trigonometric Function – Example 3:

Find the exact value of trigonometric function. \(cos\) \(225^\circ\)

Solution:

Write \(cos\) \((225^\circ)\) as \(cos\) \((180^\circ+45^\circ)\). Recall that \(cos\)\(⁡180^\circ=-1\), \(cos\)\(⁡45^\circ =\frac{\sqrt{2}}{2}\)
\(225^\circ\) is in the third quadrant and \(cos\) is negative in the quadrant \(3\). The reference angle of \(225^\circ\) is \(45^\circ\). Therefore, \(cos\) \(225^\circ=-\frac{\sqrt{2}}{2}\)

Evaluating Trigonometric Function – Example 4:

Find the exact value of trigonometric function. \(tan\) \(\frac{7π}{6}\)

Solution:

Rewrite the angles for \(tan\) \( \frac{7π}{6} \):
\(tan\) \(\frac{7π}{6}=\) \(tan\) \((\frac{6π+π}{6})=tan⁡(π+\frac{1}{6} π) \)
Use the periodicity of \(tan\): \(tan\)\((x+π .k)=\) \(tan\)\((x)\)
\( tan⁡(π+\frac{1}{6} π)=\) \(tan\)\(⁡(\frac{1}{6} π)=\frac{\sqrt{3}}{3}\)

Exercises for Evaluating Trigonometric Function

Find the exact value of each trigonometric function.

  • \(\color{blue}{cot \ -495^\circ=}\)
  • \(\color{blue}{tan \ 405^\circ=}\)
  • \(\color{blue}{cot \ 390^\circ=}\)
  • \(\color{blue}{cos \ -300^\circ=}\)
  • \(\color{blue}{cot \ -210^\circ=}\)
  • \(\color{blue}{tan \ \frac{7π}{6}=}\)

Download Evaluating Trigonometric Function Worksheet

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

Related to "How to Evaluate Trigonometric Function? (+FREE Worksheet!)"

How to Determine Limits Using the Squeeze Theorem?How to Determine Limits Using the Squeeze Theorem?
How to Determine Limits Using Algebraic Manipulation?How to Determine Limits Using Algebraic Manipulation?
How to Estimate Limit Values from the Graph?How to Estimate Limit Values from the Graph?
Properties of LimitsProperties of Limits
How to Find the Expected Value of a Random Variable?How to Find the Expected Value of a Random Variable?
How to Define Limits Analytically Using Correct Notation?How to Define Limits Analytically Using Correct Notation?
How to Solve Multiplication Rule for Probabilities?How to Solve Multiplication Rule for Probabilities?
How to Solve Venn Diagrams and the Addition Rule?How to Solve Venn Diagrams and the Addition Rule?
How to Find the Direction of Vectors?How to Find the Direction of Vectors?
Vectors IntroductionVectors Introduction

What people say about "How to Evaluate Trigonometric Function? (+FREE Worksheet!)"?

No one replied yet.

Leave a Reply