Trigonometry and Quadratics Quiz

Radians and Degrees

• 360 degrees is equivalent to 2π radians.
• In a unit circle, the circumference is C=2π, which also represents 360 degrees.

45-45-90 Triangle

• The hypotenuse measures 1 (radius of a unit circle).
• The lengths of the other two sides are both √½, derived using the Pythagorean theorem.

Completing the Square

• A method used to convert a quadratic equation into a perfect square trinomial for easier solving.

Symmetry in Functions

• The cosine function exhibits y-axis symmetry, allowing reflection of quadrants 2 and 3 across the y-axis to quadrants 1 and 4.
• The sine function is symmetric with respect to the origin, permitting a 180-degree rotation of quadrants 2 and 3 to quadrants 4 and 1.

Inverse Functions

• Finding an inverse function typically involves swapping the input and output values in the equation and solving for the new output.

Reference Angles

• Useful for determining trigonometric identities as an angle and its reference angle share the same sine, cosine, and tangent values.
• Positive or negative signs of these trigonometric values may vary depending on the quadrant.

Definition of Reference Angle

• The smallest angle formed by the terminal side of an angle with the x-axis.

Trigonometric Identity Signs

• Memorization tool: "All Strippers Take Cash" indicates which trigonometric ratios are positive in each quadrant.

Coordinates on the Unit Circle

• Coordinates based on angle or reference angle determined via cosine and sine values, represented as (cosine, sine).
• The order of cosine before sine aligns with their alphabetical arrangement.

Standard Deviation Formulas

• For population proportions, the formula is represented as p (population proportion).
• For sample means, σ represents sample standard deviation, with σ sub x denoting standard deviation.

Probability of Coin Flips

• The probability of flipping 2 heads consecutively is calculated as (1/2)(1/2) = 1/4.
• The first flip's success rate is 50%, and the same applies to the second flip, leading to a combined chance of 1/4.

Percent Rate of Change

• Also referred to as the growth or decay factor, capturing the rate of change in percentage terms.

Definition of a Parabola

• A parabola is defined as the set of all points where the distance to a fixed point (focus) equals the distance to a fixed line (directrix).