## 1. Cyclic Function/Trigonometric Function y=1.5sin(2/3x)+3.5. A cyclic function is a function that has a graph that could go on forever, a trigonometric function is one that may not go on forever.

### 1.1. 1.5 = amplitude: the maximum height of the graph minus the minimum height of the graph divided by 2. (basically, the midline of the graph)

### 1.2. 2/3 = the "b" changes the horizontal stretch/compression, its the number of cycles in 2π, using the equation b=2π/p. 2π is one cycle and p represents the period. the period is the length of one cycle. in this case, there is a period of 3π. So 2π/3π = 2/3.

## 2. Unit Circle: A unit circle is a circle with a radius of one (a unit radius). In trigonometry, the unit circle is centered at the origin. the x value (or the horizontal distance) is cosϑ and the y value (or the vertical distance) is sinϑ.

### 2.1. Degrees

2.1.1. Ex: 3π/4 - a degree is one way to plot all 360° on a unit circle (with 15° intervals). The way to turn this into a degree, us you multiply the radian by 180/π. This will give you 135°

### 2.2. Radians

2.2.1. Ex: 135° - a radian is equal to 180/π. The radius of a unit circle (the cos value) joined with the vertical distance of the arc from zero (the sine value) create an angle and that angle is 1 radian.

## 3. Sine/Cosine/Tangent

### 3.1. Sine - sine is the vertical distance whether it be going up (positive) or going down (negative). to solve for sine, you use the equation Soh. which translates to Sineϑ=Opposite/Hypotenuse. The opposite and hypotenuse are sides of a triangle. once you find sine, (and hypotenuse was already given) you can use the pythagorean theory to solve for the hypotenuse of a triangle. (a^2 + b^2 = c^2).

### 3.2. Cosine - cosine is the horizontal distance whether it be going left (negative) or right (positive). to solve for cosine, you use the equation Cah. which translates to Cosϑ=adjacent/hypotenuse. once you find cosine, (and the hypotenuse was already given) you can use the pythagorean theory to solve for the sine (vertical distance) of a triangle and use that to find the points on a unit circle.

3.2.1. like (x,y) points on a graph, a unit circle has (cosϑ,sinϑ) points on a unit circle. After using the Soh or Cah to find the sineϑ or cosϑ, you will result in points like (1/2, sqrt(3)/2)