trig

Here are the flashcards for the high-priority formulas we covered, including their purpose and the crucial rule to remember for the test.

🃏 AAF Formula Flashcards

1. Trigonometry: Law of Sines

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| Front | \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} | Used to find missing sides or angles in non-right triangles when you have an angle and its opposite side (AAS or ASA cases). | You must have a pair of angle and opposite side to start the proportion. |

2. Trigonometry: Law of Cosines

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| Front | c^2 = a^2 + b^2 - 2ab \cos(C) | Used to find a missing side when you have two sides and the included angle (SAS case), or to find an angle when you have all three sides (SSS case). | The angle (C) must be between the two sides (a and b) in the formula. |

3. Trigonometry: Arc Length

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| Front | s = r \theta | Used to find the length (s) of a section of a circle's circumference, given the radius (r). | The angle (\theta) must be in radians. Use \frac{\pi}{180^\circ} to convert degrees. |

4. Geometry: Standard Form of a Circle

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| Front | (x - h)^2 + (y - k)^2 = r^2 | Defines a circle on a coordinate plane. Used to identify the center and radius. | The center coordinates (h, k) are always the opposite sign of the numbers in the parentheses. |

5. Advanced Algebra: Quadratic Vertex

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| Front | h = \frac{-b}{2a} | Used to find the x-coordinate (h) of the vertex (max or min point) for a quadratic f(x) = ax^2 + bx + c. | Watch the negative sign! It is negative negative b if b is negative. $|6. Advanced Algebra: Logarithmic Rules| Side | Formula | Purpose | Key Rule ||---|---|---|---|| Front | \log_b(y) = x \longleftrightarrow b^x = y | Converts between logarithmic form and exponential form to solve equations. | The argument (y) of the logarithm must be > 0. Reject any x-solution that makes the argument zero or negative. |7. Geometry: Volume of Similar Figures| Side | Formula | Purpose | Key Rule ||---|---|---|---|| Front | \frac{V_B}{V_A} = k^3 | Finds the ratio of volumes (V_B to V_A) when the figures are similar. | The volume ratio is the cube (k^3) of the linear ratio (k).$ |

8. Geometry: Distance Formula

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| Front | d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} | Calculates the distance (d) between any two points (x_1, y_1) and (x_2, y_2) on a coordinate plane. | The formula is the Pythagorean Theorem dressed up; remember the \Delta x and \Delta y terms must be squared before adding. |