Tangent function CVU2024

...the opposite side to the adjacent side for a given angle measurement.

...the adjacent side to the opposite side for a given angle measurement.

...the adjacent side to the hypotenuse for a given angle measurement.

...the opposite side to the hypotenuse for a given angle measurement.

Tangent is the distance for a given angle measurement.

Tangent is the rise and run for a given angle measurement.

Tangent is the midpoint for a given angle measurement.

Tangent is the size of a given angle measurement.

the 1st and 2nd quadrants

the 1st and 3rd quadrants

the 1st and 4th quadrants

the 2nd and 3rd quadrants

$$\frac{opposite}{hypotenuse}$$  

$$\frac{opposite}{adjacent}$$  

$$\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$$  

$$\frac{hypotenuse}{adjacent}$$  

-√2/2

1

√2/2

-1

.87

1.7

.5

.11

$$\tan0$$

$$\tan\left(\frac{\pi}{2}\right)$$

$$\tan\left(\frac{2\pi}{3}\right)$$

$$\tan\left(2\pi\right)$$

down 2

up 2

up 5

no vertical translation

(-∞, ∞)

[-1, 1]

(0, ∞)

(-∞, 0)

$$x=0\ and\ x=2\pi$$  

$$\ x=\frac{\pi}{2}\ and\ x=\frac{3\pi}{2}$$  

$$x=\sqrt{3}\ and\ x=-3$$  

$$\ x=\frac{\pi}{2}\ and\ x=2\pi$$  

$$\frac{2}{\sqrt{3}}$$  

$$\frac{\sqrt{2}}{2}$$  

$$-\sqrt{3}$$  

$$-\frac{\sqrt{3}}{3}$$  

y=6tan(8x)

y=6tan(4x)

y=6tan1/4x

y=6tanx

$$y=\tan\left(\frac{1}{2}x\right)$$

$$y=\tan\left(2x\right)$$

$$y=\tan\left(\frac{1}{4}x\right)$$

$$y=\tan\left(4x\right)$$

y = tan (2x) + 5

y = tan (x) - 5

y = tan (1/2x) - 5

y = tan (1/2x) + 5

Tangent has no amplitude

always 1

always $$\pi$$

It varies with each graph

π/5

π

5

5π

2π/5