Graphs of Trig Functions

Some new trigonometric functions...

• $$\sec x = \frac{1}{\cos x} \text{ the secant.}$$
• $$\csc x = \frac{1}{\sin x} \text{ the cosecant.}$$
• $$\cot x = \frac{1}{\tan x} = \frac{\cos x}{\sin x} \text{ the cotangent.}$$

We've seen graphs of sine and cosine:
-- $\sin(x)$
-- $\cos(x)$
Which graph is the green line?
$\tan(x)= \sin(x)/\cos(x)$?
$\sec(x)= 1/\cos(x)$?
$\csc(x)= 1/\sin(x)$?

-- $\sin(x)$
-- $\cos(x)$
Which graph is the orange line?
$\tan(x)= \sin(x)/\cos(x)$?
$\sec(x)= 1/\cos(x)$?
$\csc(x)= 1/\sin(x)$?

-- $\sin(x)$
-- $\cos(x)$
Which graph is the gray line?
$\tan(x)= \sin(x)/\cos(x)$?
$\sec(x)= 1/\cos(x)$?
$\csc(x)= 1/\sin(x)$?

Pythagorean identity

If $r=1$, then

• The side of the triangle adjacent to $\theta$ has length $\cos \theta$,
• The opposite side has length $\sin\theta$.

Pythagoras says... $$(\sin\theta)^2+(\cos\theta)^2 = 1^2=1.$$

Special triangles

Another problem