Periodic functions

Periodic functions > The sine function

123456The sine function

Exercises

Exercise 1

Given is the graph of $f (x) = sin (x)$ .
Solve the following equations. Give exact answers where possible, give an approximation in three decimals otherwise.

$sin (x) = 0,35$

$sin (x) = -0,35$

$sin (x) = \frac{1}{2} \sqrt{3}$

$sin (x) = - \frac{1}{2} \sqrt{2}$

Exercise 2

Give all solutions:

$sin (x) = 1$

$sin (x) = sin (1)$

$sin (1) = x$

Exercise 3

Given is the function $f$ with $f (x) = 2 sin (x) - 1$ op $[0, 4 π]$ .

Compute all zeroes of the graph of this function.

Solve: $f (x) \geq 0$ .

Exercise 4

Given is function $g$ with $g (x) = sin (2 x)$ on $[0, 4 π]$ .

Solve: $g (x) = 0,5$

Solve: $g (x) \geq 0,5$ .

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