Graphing Trigonometric Functions with Domain and Range

Key Questions

How do I graph a trig function?

Answer:

Using a graphing calculator: MODE must be in radians

Explanation:

Using a graphing calculator: MODE must be in radians.

On a TI graphing calculator, with the standard zoom, $Y 1 = sin (x)$ $Y1 = sin(x)$ :

graph{sin(x) [-10.04, 9.96, -5.16, 4.84]}

On a TI graphing calculator, with the standard zoom, $Y 1 = cos (x)$ $Y1 = cos(x)$ :

graph{cosx [-10.04, 9.96, -5.16, 4.84]}

On a TI graphing calculator, with the standard zoom, $Y 1 = tan (x)$ $Y1 = tan(x)$ :

graph{tan x [-10.04, 9.96, -5.16, 4.84]}

On a TI graphing calculator, with the standard zoom, $y = sec (x) : Y 1 = \frac{1}{cos (x)}$ $y = sec(x): Y1 = 1/(cos(x))$ :

graph{1/(cos x) [-10.04, 9.96, -5.16, 4.84]}

On a TI graphing calculator, with the standard zoom, $y = csc (x) : Y 1 = \frac{1}{sin (x)}$ $y = csc(x): Y1 = 1/(sin(x))$ :

graph{1/(sin x) [-10.04, 9.96, -5.16, 4.84]}

On a TI graphing calculator, with the standard zoom, $y = cot (x) : Y 1 = \frac{1}{tan (x)}$ $y = cot(x): Y1 = 1/(tan(x))$ :

graph{1/(tan x) [-10.04, 9.96, -5.16, 4.84]}

marfre · 1 · May 8 2017
What are the six trigonometric functions of an angle?

Answer:

$sin (x)$ $sin(x)$ , $cos (x)$ $cos(x)$ , $tan (x)$ $tan(x)$ , $csc (x)$ $csc(x)$ , $sec (x)$ $sec(x)$ , $cot (x)$ $cot(x)$ .

Explanation:

$cos (x) = sin (\frac{π}{2} - x)$ $cos(x)=sin(pi/2-x)$

$tan (x) = \frac{sin (x)}{cos (x)}$ $tan(x)=frac{sin(x)}{cos(x)}$

$csc (x) = \frac{1}{sin (x)}$ $csc(x)=1/sin(x)$

$sec (x) = \frac{1}{cos (x)}$ $sec(x)=1/cos(x)$

$cot (x) = \frac{1}{tan (x)}$ $cot(x)=1/tan(x)$

Bio · 1 · Oct 31 2015
What are the six trigonometric functions of a right triangle?

Given a right triangle, select a vertex where the hypotenuse and one of the legs meet.

The angle $θ$ $theta$ created by this two sides will be used as a reference point

The side that formed the angle $θ$ $theta$ together with the hypotenuse will be referred to as $a d j a c e n t$ $adjacent$ (side adjacent to the angle). The other side will be referred to as $o p p o s i t e$ $opposite$ (side opposite the angle)

The ratio between the $o p p o s i t e$ $opposite$ and the $hypotenuse$ $"hypotenuse"$ is called $sine (sin$ $"sine" (sin$ ). The inverse of this ratio is called $cosecant (csc$ $"cosecant" (csc$ )

$sin θ = \frac{opposite}{hypotenuse}$ $sin theta = "opposite" / "hypotenuse"$

$csc θ = \frac{hypotenuse}{opposite} = \frac{1}{sin θ}$ $csc theta = "hypotenuse" / "opposite" = 1 / sin theta$

The ratio between the $a d j a c e n t$ $adjacent$ and the $hypotenuse$ $"hypotenuse"$ is called "cosine". The inverse of this ratio is called "secant"

$cos θ = \frac{adjacent}{hypotenuse}$ $cos theta = "adjacent" / "hypotenuse"$

$sec θ = \frac{hypotenuse}{adjacent} = \frac{1}{cos θ}$ $sec theta = "hypotenuse" / "adjacent" = 1 / cos theta$

The ratio between the $o p p o s i t e$ $opposite$ and the $a d j a c e n t$ $adjacent$ is called
$tangent$ $"tangent"$ . The inverse of this ratio is called $cotangent$ $"cotangent"$

$tan θ = \frac{opposite}{adjacent}$ $tan theta = "opposite" / "adjacent"$

$cot θ = \frac{adjacent}{opposite} = \frac{1}{tan θ}$ $cot theta = "adjacent" / "opposite" = 1 / tan theta$

For example, in a 30-60-90 triangle

$sin 30 = \frac{1}{2}$ $sin 30 = 1 / 2$
$cos 30 = \frac{3^{\frac{1}{2}}}{2}$ $cos 30 = 3^(1/2)/2$
$tan 30 = \frac{1}{3^{\frac{1}{2}}}$ $tan 30 = 1 / 3^(1/2)$
$csc 30 = 2$ $csc 30 = 2$
$sec 30 = \frac{2}{3^{\frac{1}{2}}}$ $sec 30 = 2/3^(1/2)$
$cot 30 = 3^{\frac{1}{2}}$ $cot 30 = 3^(1/2)$

$sin 60 = \frac{3^{\frac{1}{2}}}{2}$ $sin 60 = 3^(1/2)/2$
$cos 60 = \frac{1}{2}$ $cos 60 = 1 /2$
$tan 60 = 3^{\frac{1}{2}}$ $tan 60 = 3^(1/2)$
$csc 60 = \frac{2}{3^{\frac{1}{2}}}$ $csc 60 = 2/3^(1/2)$
$sec 60 = 2$ $sec 60 = 2$
$cot 60 = \frac{1}{3^{\frac{1}{2}}}$ $cot 60 = 1 / 3^(1/2)$

seph · · Oct 11 2014