Summary

Trigonometry

Trigonometry concepts revolve around:

degrees
the ability to get what we want to find (x length or y height) in the triangles given values in the triangle whether we want to find what side (sin, cos, tan, etc..)
radian
- 360°: A full circle is $2\pi$ (about 6.28 radii).
- 90°: Half of $\pi$ is $\pi / 2$ (about 1.57 radii).
- 45°: Half of $\pi / 2$ is $\pi / 4$ (about 0.785 radii).
unit circle
- imagine triangle in circle and rotate that triangle

Simplifying and Factoring: Breaking down complex expressions into their simplest forms or constituent “building blocks” (e.g., $(x+2)(x-3)$ ).
Solving for Variables (“Finding $x$ ”): Using inverse operations to isolate an unknown value within an equation.
Real-World Modeling: Translating physical situations, like financial growth or physics, into mathematical equations.
Graphical Visualization: Plotting equations on a coordinate plane to identify patterns, intercepts, and points of intersection.
Equation Forms: Categorizing relationships based on their structure, such as Linear (constant change), Quadratic (parabolic curves), and Polynomial (multiple terms).
Function Types and Number Systems: Working with different mathematical “species,” including Exponents, Logarithms, Absolute Values, and Complex Numbers ( $i = \sqrt{-1}$ ).
Inequalities: Solving and graphing expressions where one side is “greater than” or “less than” the other, rather than just equal.
Systems of Equations: Solving for multiple variables simultaneously where two or more equations overlap.
Sequences and Series: Identifying patterns in lists of numbers and calculating their sums, which is essential for understanding limits in Calculus.
Rearranging Formulas (Literal Equations): The ability to transform an equation to highlight a different variable (e.g., changing $F = ma$ to $a = F/m$ ), which is a core skill for engineering.