Trigonometry Examples

$y = \sin (\frac{1}{2}) (x - 2 π)$

Step 1

Write $y = \sin (\frac{1}{2}) (x - 2 π)$ as a function.

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

Step 2

Simplify.

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Step 2.1

Evaluate $\sin (\frac{1}{2})$ .

$f (x) = 0.47942553 (x - 2 π)$

Step 2.2

Apply the distributive property.

$f (x) = 0.47942553 x + 0.47942553 (- 2 π)$

Step 2.3

Multiply $0.47942553 (- 2 π)$ .

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Step 2.3.1

Multiply $- 2$ by $0.47942553$ .

$f (x) = 0.47942553 x - 0.95885107 π$

Step 2.3.2

Multiply $- 0.95885107$ by $π$ .

$f (x) = 0.47942553 x - 3.0123195$

Step 3

Find $f (- x)$ .

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Step 3.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = 0.47942553 (- x) - 3.0123195$

Step 3.2

Multiply $- 1$ by $0.47942553$ .

$f (- x) = - 0.47942553 x - 3.0123195$

Step 4

A function is even if $f (- x) = f (x)$ .

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Step 4.1

Check if $f (- x) = f (x)$ .

Step 4.2

Since $- 0.47942553 x - 3.0123195$ $\neq$ $0.47942553 x - 3.0123195$ , the function is not even.

The function is not even

Step 5

A function is odd if $f (- x) = - f (x)$ .

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Step 5.1

Find $- f (x)$ .

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Step 5.1.1

Multiply $0.47942553 x - 3.0123195$ by $- 1$ .

$- f (x) = - (0.47942553 x - 3.0123195)$

Step 5.1.2

Apply the distributive property.

$- f (x) = - (0.47942553 x) + 3.0123195$

Step 5.1.3

Multiply.

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Step 5.1.3.1

Multiply $0.47942553$ by $- 1$ .

$- f (x) = - 0.47942553 x + 3.0123195$

Step 5.1.3.2

Multiply $- 1$ by $- 3.0123195$ .

$- f (x) = - 0.47942553 x + 3.0123195$

Step 5.2

Since $- 0.47942553 x - 3.0123195$ $\neq$ $- 0.47942553 x + 3.0123195$ , the function is not odd.

The function is not odd

Step 6

The function is neither odd nor even

Step 7