Triginometry

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Units

Unit 1: 

Angles:

How to measure in both degrees and radians

Know the conversion between degrees and radian measure

4.1

Sine and Cosine:

  • Their definition as x- & y-coordinates on the unit circle
  • Their graphs as functions and the characteristics
  • Students are capable of computing unknown sides or angles in a right triangle.
  • Students use trigonometry in a variety of word problems.
4.2, 4.3, 4.8

Unit 2 
Functions of the form f(t)=A sin (Bt + C) & f(t)=A cos (Bt + C):

  • Graphing
  • Properties: amplitude, frequency, period and phase shift (A, B & C)
  • Student will be able to take a given angle and compute the trigonometric function and its inverse with the aid of the unit circle (by hand)
  • Students use trigonometry in a variety of word problems.


4.4, 4.5, 4.7, 4.8

Unit 3:

 Analytical Trigonometry:

  • Fundamental Identities
  • Sum and Difference Formulas
  • Use double-angle and half-angle formulas to prove and/or simplify other trigonometric identities.
5.1, 5.2, 5.3, 5.4

Analytical Trigonometry:

  • Students will be familiar with the law of sines and law of cosines to solve problems
5.5, 5.6

Unit 4: 

Applications of Trigonometry:

  • Students need to know how to write equations in rectangular coordinates in terms of polar coordinates.
  • Vectors
  • Parametric Relations
6.1, 6.2, 6.3, 6.4, 6.5

Unit 1

Angles

  • An angle is measured in degrees.
  • A radian's measurement is where the radius is the same length as the arc length.

  • To convert to radians, you multiply the degree by pi over 180
  • To convert to degrees, you multiply by 180 over pi.


On the unit circle the the x is represented as Cosine and the y is represented as the Sine. 

Sines and Cosines

With sine graphs, they always start at the origin.

The formula for graphing a sine graph is  

y = A sin(B(x - C)) + D, 

|A| = amplitude
B = cycles from 0 to 2pi
period = 2 pi over B
D = vertical shift (or displacement)
C = horizontal shift (sometimes called "phase shift" when B = 1)

Example

This problem is also a combination of dealing with the values of A and B.  The A value of 1/2 tells us that the graph will have a vertical shrink and an amplitude of 1/2.  The B value of 3 tells us that 3 complete cycles of the graph will be seen in the standard domain of  0 to (there will be a horizontal shrink).

The period of this new graph will be (or 120º).

Finding the Side

Here you see the use of the Term SOH CAH TOA to find the missing side.

Here is an example of finding the missing side using the formula.

Unit 2

Video