Find the Other Trig Values in Quadrant III cos(theta)=0

$\cos (θ) = 0$

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

$\cos (θ) = \frac{adjacent}{hypotenuse}$

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

$Opposite = - \sqrt{{hypotenuse}^{2} - {adjacent}^{2}}$

Replace the known values in the equation.

$Opposite = - \sqrt{{(1)}^{2} - {(0)}^{2}}$

Simplify inside the radical.

Tap for more steps...

Negate $\sqrt{{(1)}^{2} - {(0)}^{2}}$ .

Opposite $= - \sqrt{{(1)}^{2} - {(0)}^{2}}$

One to any power is one.

Opposite $= - \sqrt{1 - {(0)}^{2}}$

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

Opposite $= - \sqrt{1 - 0}$

Multiply $- 1$ by $0$ .

Opposite $= - \sqrt{1 + 0}$

Add $1$ and $0$ .

Opposite $= - \sqrt{1}$

Any root of $1$ is $1$ .

Opposite $= - 1 \cdot 1$

Multiply $- 1$ by $1$ .

Opposite $= - 1$

Find the value of sine.

Tap for more steps...

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

$\sin (θ) = \frac{opp}{hyp}$

Substitute in the known values.

$\sin (θ) = \frac{- 1}{1}$

Divide $- 1$ by $1$ .

$\sin (θ) = - 1$

Find the value of tangent.

Tap for more steps...

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

$\tan (θ) = \frac{opp}{adj}$

Substitute in the known values.

$\tan (θ) = \frac{- 1}{0}$

Division by $0$ results in tangent being undefined at $θ$ .

$\tan (θ) = Undefined$

Undefined

Find the value of cotangent.

Tap for more steps...

Use the definition of cotangent to find the value of $\cot (θ)$ .

$\cot (θ) = \frac{adj}{opp}$

Substitute in the known values.

$\cot (θ) = \frac{0}{- 1}$

Divide $0$ by $- 1$ .

$\cot (θ) = 0$

Find the value of secant.

Tap for more steps...

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

$\sec (θ) = \frac{hyp}{adj}$

Substitute in the known values.

$\sec (θ) = \frac{1}{0}$

Division by $0$ results in secant being undefined at $θ$ .

$\sec (θ) = Undefined$

Undefined

Find the value of cosecant.

Tap for more steps...

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

$\csc (θ) = \frac{hyp}{opp}$

Substitute in the known values.

$\csc (θ) = \frac{1}{- 1}$

Divide $1$ by $- 1$ .

$\csc (θ) = - 1$

This is the solution to each trig value.

Undefined

Do you know how to Find the Other Trig Values in Quadrant III cos(theta)=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.