Aug 30, 2024

- Discussed trigonometry functions, starting with basic angles.
- How to use reference angles to find trigonometry functions of any angle.
- Graphing trigonometry functions and understanding their behavior.

- An angle is typically measured in reference to the x-axis.
**Initial side:**where the angle starts.**Terminal side:**where the angle ends.- Positive angles: counterclockwise rotation.
- Negative angles: clockwise rotation.

- Two main systems: Degrees and Radians.
**Radians**involve pi, an irrational number representing the relationship between a circle's diameter and circumference.**Degrees**are more commonly used for everyday angle measurement.

**Equation:**2π radians = 360 degrees.- Convert degrees to radians: multiply by π/180.
- Convert radians to degrees: multiply by 180/π.

- Understanding angles in a unit circle and graphing on the XY-axis.
**Co-terminal angles:**Angles with the same terminal side.

- Trig functions relate the angles of a right triangle to ratios of its sides.
**Sine (sin):**Opposite over Hypotenuse.**Cosine (cos):**Adjacent over Hypotenuse.**Tangent (tan):**Opposite over Adjacent.**Cosecant (csc):**Hypotenuse over Opposite (reciprocal of sin).**Secant (sec):**Hypotenuse over Adjacent (reciprocal of cos).**Cotangent (cot):**Adjacent over Opposite (reciprocal of tan).

**Unit Circle:**Radius of one.- The x-coordinate represents cos, and the y-coordinate represents sin.
**Tangent:**y/x, or sin/cos.

**Mnemonic:**All Students Take Calculus (ASTC)- Quadrant I: All trig functions positive.
- Quadrant II: Only sin and cosec are positive.
- Quadrant III: Only tan and cot are positive.
- Quadrant IV: Only cos and sec are positive.

- A reference angle is the acute angle that the terminal side of a given angle makes with the x-axis.
- Used to find trig functions of any angle by assessing the quadrant location and using ASTC.

- Important for solving equations and expressions.
**Sine and Cosine relationship:**sin²θ + cos²θ = 1.**Tangent identity:**tanθ = sinθ/cosθ.

- Understand the structure of sine, cosine, and tangent graphs.
**Amplitude and Period: Key Concepts**- Amplitude: Height from the center line to the peak.
- Period: How long it takes for the function to repeat.

**Vertical Stretch or Compression:**Changes to amplitude.**Horizontal Stretch or Compression:**Changes to period.**Phase Shift (Horizontal Shift):**Based on modifications inside the function argument.- Positive indicates left shift, negative indicates right shift.

- Applying concepts of amplitude, period, and shifts to graph sine and cosine functions.
- Ensures understanding of translation and how it affects graph placement.

- Reinforce the importance of understanding unit circle values.
- Encouragement to review trigonometry identities for calculus applications.