Trigonometry Examples

$(0, \frac{π}{2})$

Step 1

To find the $\cos (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(0, \frac{π}{2})$ , draw the triangle between the three points $(0, 0)$ , $(0, 0)$ , and $(0, \frac{π}{2})$ .

Opposite : $\frac{π}{2}$

Adjacent : $0$

Step 2

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

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Step 2.1

Raising $0$ to any positive power yields $0$ .

$\sqrt{0 + {(\frac{π}{2})}^{2}}$

Step 2.2

Apply the product rule to $\frac{π}{2}$ .

$\sqrt{0 + \frac{π^{2}}{2^{2}}}$

Step 2.3

Raise $2$ to the power of $2$ .

$\sqrt{0 + \frac{π^{2}}{4}}$

Step 2.4

Add $0$ and $\frac{π^{2}}{4}$ .

$\sqrt{\frac{π^{2}}{4}}$

Step 2.5

Rewrite $\sqrt{\frac{π^{2}}{4}}$ as $\frac{\sqrt{π^{2}}}{\sqrt{4}}$ .

$\frac{\sqrt{π^{2}}}{\sqrt{4}}$

Step 2.6

Pull terms out from under the radical, assuming positive real numbers.

$\frac{π}{\sqrt{4}}$

Step 2.7

Simplify the denominator.

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Step 2.7.1

Rewrite $4$ as $2^{2}$ .

$\frac{π}{\sqrt{2^{2}}}$

Step 2.7.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{π}{2}$

Step 3

$\cos (θ) = \frac{Adjacent}{Hypotenuse}$ therefore $\cos (θ) = \frac{0}{\frac{π}{2}}$ .

$\frac{0}{\frac{π}{2}}$

Step 4

Simplify $\cos (θ)$ .

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$\cos (θ) = 0 (\frac{2}{π})$

Step 4.2

Multiply $0$ by $\frac{2}{π}$ .

$\cos (θ) = 0$