Transcript Document

11th grade
Trigonometry
Ms. Kavanaugh
The period for the sine graph is 2𝜋, meaning the graph
completes one whole wave every 2𝜋. The normal sine
graph, for one period, begins at the origin, (0,0), and ends at
the point (2𝜋,0). The amplitude of the sine function is 1. It’s
maximum on the y-scale is 1 and the minimum is -1.
The period for the cosine graph is 2𝜋, meaning the graph
completes one whole wave every 2𝜋. The normal cosine
graph, for one period, begins at (0,1) and ends at the point
(2𝜋,1). The amplitude of the cosine function is 1. It’s
maximum on the y-scale is 1 and the minimum is -1.
The period of the tangent graph is 𝜋. Meaning the graph
completes one whole wave every 𝜋. Unlike the sine and cosine
functions, tangent does not have an amplitude. Instead the
function has asymptotes one intervals of 𝜋. This happens because
of the definition of tan x. When cos x =0, the graph is undefined
causing an asymptote.
Remember:
Tan x = sinx/cosx
The cosecant graph has a period of 2𝜋. Meaning it completes
one wave every 2𝜋. Similarly to the tangent graph, the csc
graph has vertical asymptotes. This happens because of the
definition of csc x. When sinx =0, the graph is undefined
causing an asymptote. Because of these asymptotes, the
cosecant graph does not have an amplitude.
Remember:
Csc x = 1/sinx
The secant graph has a period of 2𝜋. Meaning it completes
one wave every 2𝜋. Similar to the tangent graph, the sec
graph has vertical asymptotes. This happens because of the
definition of sec x. When cosx =0, the graph is undefined
causing an asymptote. Because of these asymptotes, the
secant graph does not have an amplitude.
Remember:
secx= 1/cosx
The cotangent graph has a period of 𝜋. Meaning the graph
completes one whole wave every 𝜋. Like its reciprocal, the
cotangent has vertical asymptotes. This happen because
of the definition of cotangent, when sinx =0 the function is
undefined causing an asymptote. Because of these
asymptotes, the cotangent graph does not have an
amplitude.
Remember:
cotx=cosx/sinx
Amplitude is the height of the wave. The amplitude works in
both directions. Every wave has a positive amplitude,
meaning you take the absolute value of the amplitude of the
wave. The amplitude works in both directions. The
amplitude is usually written as a numerical value in front of
the function.
The period of the function is the length in which it takes the graph one
wave to complete. The period for sine, cosine, cosecant, and secant is
found by the equation 2 𝜋/b. The period of the tangent and cotangent
is found by using 𝜋/b. Where in both cases b is the numerical value
found directly after the function, usually contained inside the
parenthesis.
Remember that the sine functions
starts at the origin. For this
function the amplitude is 3 and the
period is 𝜋. Go back to the
question and give it another try!
Remember that the tangent function
has vertical asymptotes. There is no
amplitude for this function and the
period is 𝜋/3. Click the arrow to go
back to the question and give it
another go!
This is a cosine function with
an amplitude of 3, and a
period of 𝜋. Click the arrow to
finish this lesson.
Congratulations, you’ve completed this lesson on the
three trig functions and their reciprocals! Click the
star to go back to the main menu.