Find the Other Trig Values in Quadrant IV cot(x)=-8/15

$\cot (x) = - \frac{8}{15}$

Use the definition of cotangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

$\cot (x) = \frac{adjacent}{opposite}$

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

$Hypotenuse = \sqrt{{opposite}^{2} + {adjacent}^{2}}$

Replace the known values in the equation.

$Hypotenuse = \sqrt{{(- 15)}^{2} + {(8)}^{2}}$

Simplify inside the radical.

Raise $- 15$ to the power of $2$ .

Hypotenuse $= \sqrt{225 + {(8)}^{2}}$

Raise $8$ to the power of $2$ .

Hypotenuse $= \sqrt{225 + 64}$

Add $225$ and $64$ .

Hypotenuse $= \sqrt{289}$

Rewrite $289$ as $17^{2}$ .

Hypotenuse $= \sqrt{17^{2}}$

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

Hypotenuse $= 17$

Find the value of sine.

Use the definition of sine to find the value of $\sin (x)$ .

$\sin (x) = \frac{opp}{hyp}$

Substitute in the known values.

$\sin (x) = \frac{- 15}{17}$

Move the negative in front of the fraction.

$\sin (x) = - \frac{15}{17}$

Find the value of cosine.

Use the definition of cosine to find the value of $\cos (x)$ .

$\cos (x) = \frac{adj}{hyp}$

Substitute in the known values.

$\cos (x) = \frac{8}{17}$

Find the value of tangent.

Use the definition of tangent to find the value of $\tan (x)$ .

$\tan (x) = \frac{opp}{adj}$

Substitute in the known values.

$\tan (x) = \frac{- 15}{8}$

Move the negative in front of the fraction.

$\tan (x) = - \frac{15}{8}$

Find the value of secant.

Use the definition of secant to find the value of $\sec (x)$ .

$\sec (x) = \frac{hyp}{adj}$

Substitute in the known values.

$\sec (x) = \frac{17}{8}$

Find the value of cosecant.

Use the definition of cosecant to find the value of $\csc (x)$ .

$\csc (x) = \frac{hyp}{opp}$

Substitute in the known values.

$\csc (x) = \frac{17}{- 15}$

Move the negative in front of the fraction.

$\csc (x) = - \frac{17}{15}$

This is the solution to each trig value.

$\sin (x) = - \frac{15}{17}$

$\cos (x) = \frac{8}{17}$

$\tan (x) = - \frac{15}{8}$

$\cot (x) = - \frac{8}{15}$

$\sec (x) = \frac{17}{8}$

$\csc (x) = - \frac{17}{15}$

Find the Other Trig Values in Quadrant IV cot(x)=-8/15

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