Find the Sine Given the Point (1,-6)

$(1, - 6)$

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(1, - 6)$ , draw the triangle between the three points $(0, 0)$ , $(1, 0)$ , and $(1, - 6)$ .

Opposite : $- 6$

Adjacent : $1$

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

One to any power is one.

$\sqrt{1 + {(- 6)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{1 + 36}$

Add $1$ and $36$ .

$\sqrt{37}$

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{- 6}{\sqrt{37}}$ .

$\frac{- 6}{\sqrt{37}}$

Simplify $\sin (θ)$ .

Move the negative in front of the fraction.

$\sin (θ) = - \frac{6}{\sqrt{37}}$

Multiply $\frac{6}{\sqrt{37}}$ by $\frac{\sqrt{37}}{\sqrt{37}}$ .

$\sin (θ) = - (\frac{6}{\sqrt{37}} \cdot \frac{\sqrt{37}}{\sqrt{37}})$

Combine and simplify the denominator.

Multiply $\frac{6}{\sqrt{37}}$ by $\frac{\sqrt{37}}{\sqrt{37}}$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{\sqrt{37} \sqrt{37}}$

Raise $\sqrt{37}$ to the power of $1$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{\sqrt{37} \sqrt{37}}$

Raise $\sqrt{37}$ to the power of $1$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{\sqrt{37} \sqrt{37}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin (θ) = - \frac{6 \sqrt{37}}{{\sqrt{37}}^{1 + 1}}$

Add $1$ and $1$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{{\sqrt{37}}^{2}}$

Rewrite ${\sqrt{37}}^{2}$ as $37$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{37}$ as $37^{\frac{1}{2}}$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{{(37^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{37^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\sin (θ) = - \frac{6 \sqrt{37}}{37^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\sin (θ) = - \frac{6 \sqrt{37}}{37^{\frac{2}{2}}}$

Rewrite the expression.

$\sin (θ) = - \frac{6 \sqrt{37}}{37}$

Evaluate the exponent.

$\sin (θ) = - \frac{6 \sqrt{37}}{37}$

Approximate the result.

$\sin (θ) = - \frac{6 \sqrt{37}}{37} \approx - 0.98639392$

Find the Sine Given the Point (1,-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.