Trigonometry Examples

$(1, - 1)$

Step 1

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

Opposite : $- 1$

Adjacent : $1$

Step 2

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

Tap for more steps...

Step 2.1

One to any power is one.

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

Step 2.2

Raise $- 1$ to the power of $2$ .

$\sqrt{1 + 1}$

Step 2.3

Add $1$ and $1$ .

$\sqrt{2}$

Step 3

$\csc (θ) = \frac{Hypotenuse}{Opposite}$ therefore $\csc (θ) = \frac{\sqrt{2}}{- 1}$ .

$\frac{\sqrt{2}}{- 1}$

Step 4

Simplify $\csc (θ)$ .

Tap for more steps...

Step 4.1

Move the negative one from the denominator of $\frac{\sqrt{2}}{- 1}$ .

$\csc (θ) = - 1 \cdot \sqrt{2}$

Step 4.2

Rewrite $- 1 \cdot \sqrt{2}$ as $- \sqrt{2}$ .

$\csc (θ) = - \sqrt{2}$

Step 5

Approximate the result.

$\csc (θ) = - \sqrt{2} \approx - 1.41421356$