Pre-Calculus Ch6,7,8

A unit circle is a circle of unit radius with center at origin. A circle is a closed geometric figure such that all the points on its boundary are at equal distance from its center. For a unit circle, this distance is 1 unit, or the radius is 1 unit. 

Angles in degree form

Angles in radian form which is written as pi in a faction or whole number

The amplitude of a trigonometric function is half the distance from the highest point of the curve to the bottom point of the curve.

The period of a function refers to the distance of a function's wave.

The phase shift is how far the function is shifted horizontally either to the right or left.

Identities hey are expressions that restate the same expression in a different way. In other words, the identities allow you to restate a trig expression in a different format, but one which has the exact same value.

Quotient identities are trigonometric identities that are written as fractions of the sine and cosine functions. The tangent forms a quotient identity and can be written as the sine of the angle divided by the cosine. Similarly, the cotangent can be written as the cosine of the angle divided by the sine.

eciprocal identities are the reciprocals of the three main trig functions sine, cosine, and tangent.

Pythagorean identities are identities in trig that are extensions of the Pythagorean theorem. The fundamental identity states that for any angle.

An even function is a function where the value of the function acting on an argument is the same as the value of the function when acting on the negative of the argumentIn contrast, an odd function is a function where the negative of the function's answer is the same as the function acting on the negative argument

The sum and difference formulas in trigonometry are used to find the value of the trigonometric functions at specific angles where it is easier to express the angle as the sum or difference of unique angles.

The trigonometric double angle formulas give a relationship between the basic trigonometric functions applied to twice an angle in terms of trigonometric functions of the angle itself.

A half-angle trig identity is found by using the basic trig ratios to derive the sum and difference formulas, then utilizing the sum formula to produce the double angle formulas. Finally, manipulating the double angle formula reveals the half-angle formulas.

The process of converting products into sums can make a difference between an easy solution to a problem and no solution at all. Two sets of identities can be derived from the sum and difference identities that help in this conversion

The process of converting sums into products can make a difference between an easy solution to a problem and no solution at all. Two sets of identities can be derived from the sum and difference identities that help in this conversion

The basic trig functions can be defined with ratios created by dividing the lengths of the sides of a right triangle in a specific order.

The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles. Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

Law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

How to solve triangles using only 3 pieces of given information.

The graphs for engine performance such as horsepower, heat, torque, and other factors and be converted into trig functions.

Flight Computers use right-angle trigonometry to calculate the approach angle for takeoff and landing.

Trigonometric equations are used to relight car wheel alignments so the car drives straight. Or for NASCAR, at a slight left angle.

Area of a triangle.

A special kind of vibrational motion in which the acceleration of an object is directly proportional to the negative of its displacement from its rest position.

A model that describes a phenomenon maintaining a sinusoidal component, but the amplitude of the component decreases with time to account for the damping effect.

Combining wave functions to compare or contrast them.