introduces basic TRIGONOMETRY covering the unit circle, exponential properties, as well as basic logarithmic functions.
Unit Circle
The unit circle is a circle with a radius of 1, it helps with learning about lengths and angles
**To view more about the unit circle refer to the links below
Exponential
Properties of Exponents:
Rational Exponents
What is a Rational Exponent? Simply exponents written as a fraction!
A rational exponent represents both an integer exponent and an nth root. The root is found in the denominator (like a tree, the root is at the bottom), and the integer exponent is found in the numerator.
Trig Identities
Reciprocal Identities:Trig identities defining cosecant, secant, and cotangent in terms of sine, cosine, and tangent.
Ratio Identities: Defining tangent and cotangent in terms of sine and cosine.
Pythagorean Identities: Trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.
Cofunction Identities:Trig identities showing the relationship between sine and cosine, tangent and cotangent, and secant and cosecant
**To view more trig identities refer to the links below
Logarithms
What is a logarithm? A logarithm is the power to which a number must be raised in order to get some other number
The number we are multiplying is called the "base", so we can say:
"the logarithm of 8 with base 2 is 3"
or "log base 2 of 8 is 3"
or "the base-2 log of 8 is 3"
Notice we are dealing with three numbers:
the base: the number we are multiplying (a "2" in the example above)
how many times to use it in a multiplication (3 times, which is the logarithm)
The number we want to get...8
Properties of Logs:
*Note: Log bases must be the same in order to apply these properties!!!
Product Property:
Quotient Property:
Power Property:
Natural Logarithms
What is it? A Natural logarithm is the logarithm to the base e of a number
Defining a Natural Logarithm:
The e constant or Euler's number is: e ≈ 2.71828183