Trigonometry Examples

$(3, 1)$

Step 1

To find the $\csc (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(3, 1)$ , draw the triangle between the three points $(0, 0)$ , $(3, 0)$ , and $(3, 1)$ .

Opposite : $1$

Adjacent : $3$

Step 2

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

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Step 2.1

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(1)}^{2}}$

Step 2.2

One to any power is one.

$\sqrt{9 + 1}$

Step 2.3

Add $9$ and $1$ .

$\sqrt{10}$

Step 3

$\csc (θ) = \frac{Hypotenuse}{Opposite}$ therefore $\csc (θ) = \frac{\sqrt{10}}{1}$ .

$\frac{\sqrt{10}}{1}$

Step 4

Divide $\sqrt{10}$ by $1$ .

$\csc (θ) = \sqrt{10}$

Step 5

Approximate the result.

$\csc (θ) = \sqrt{10} \approx 3.16227766$