Periodic functions

Periodic functions > Radians

123456Radians

Exercises

Exercise 1

These angles are given in degrees. Calculate the corresponding angles in radians.

$30 °, 20 °, 10 °, 270 °, 360 °, 455 °, 780 °$ .

Here the angles on the unit cicle have been given. Calculate the corresponding angles in whole degrees.

$\frac{1}{2} π; \frac{1}{3} π; \frac{3}{4} π; 1; π; 3,1416; 10 π$ .

Exercise 2

From now on (unless mentioned differently) we will assume that the variable $x$ in $sin (x)$ is expressed in radians.

Look at the graph of $f (x) = sin (x)$ on the interval $[-2 π, 4 π]$ .

Compute the exact values of $f (5 \cdot \frac{1}{6} π)$ and $5 \cdot f (\frac{1}{6} π)$ . Explain the difference.

Compute the exact values of $f (\frac{1}{4} π)$ and $f (- \frac{1}{4} π)$ . Explain the correspondence.

Use the graph to show that $sin (- x) = - sin (x)$ .

Use the graph to show that $sin (x) = sin (3 π - x)$ .

You cannot use a graph to prove anything. Using a figure in the unit circle you can. Now prove the two properties above.

Exercise 3

Given is $sin (x) = 0,6$ .

Use a unit circle to denote all values of $x$ with $0 \leq x < 2 π$ satisfying this equation.

Write down all values of $x$ satisfying the equation. Round your answers to three decimals.

Exercise 4

Given is $sin (x) = -0,5$ .

Use a unit circle to denote all values of $x$ with $0 \leq x < 2 π$ satisfying this equation.

Write down all values of $x$ satisfying the equation. Give exact values.