Trig Identities
This Mnemonic device is used to make it easier to recall the trig identities.
What is SOH CAH TOA?
This is the prefix put in front of a trig function to signify that it is inverted.
What is "arc"?
This is the Sine value at an angle of pi radians.
What is 0?
This is the amplitude of a standard sin or cos graph.
What is 1?
This trig function is defined by the ratio of the Opposite side length divided by the Hypotenuse length.
What is Sine?
The value of x in the following problem:
sin(x) = .5
What is:
x = pi/6 radians
or
x = 30 degrees?
This is the measurement 3pi/2 in degrees.
What is 315 degrees?
This is the period of a standard sin or cos graph.
What is 2pi radians or 360 degrees?
This trig function is the x value of a point P that lies on the perimeter of the Unit Circle.
What is Cosine?
This is the type of value that is found by using an inverse trig function. (e.g. Side length, angle measurement, ratio)
What is an angle measurement?
This is a co-terminal angle of 7pi/4 radians.
What is -pi/4 radians?
This is the amplitude of the function below:
4cos(3x)
What is 4?
This trig functions is defined in terms of the other two trig functions.
What is Tangent?
The graph of this inverse function has a domain of:
0 <= x <= pi
What is Arccosine?
This angle measurement returns equivalent Sine and Cosine values
What is pi/4 radians
or 45 degrees?
In the standard function written below, this represents the period.
a*sin(bx)
What is 2pi/|b|?
This trig identity is the only one to have undefined values.
What is Tangent?
For a function to be invert-able, it must be able to pass this test.
What is the Horizontal Line Test?
The poles of the Unit circle are at angle measurements that are multiples of this value
What is pi/2 radians
or 90 degrees.
The asymptotes of a tangent graph are at what angles and their multiples?
What is pi/2 and 3pi/2
or 90 and 315 degrees?