Trigonometry and Quadratics Quiz

Study Notes

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).

Description

Test your knowledge on radians, degrees, and the properties of triangles including 45-45-90 triangles. Explore concepts such as completing the square, function symmetry, inverse functions, and reference angles. This quiz is essential for mastering trigonometry and quadratic equations.