Unit+4

=Unit 4 Trigonometric Functions= ==

=Video/Resources= []

unit circle []

[]

**Objectives**
You will be able to convert between radians and degrees, find arc lengths, convert to nautical miles, and solve problems involving angular motion.
 * Key Ideas**
 * Angular motion || Line of travel ||
 * Arc length of a circle || Linear motion ||
 * Bearing || Minute (angle measure) ||
 * Central angle || Nautical mile ||
 * Course || Radian ||
 * Degree || Second (angle measure) ||

**Objectives**
You will be able to define the six trigonometric functions using the lengths of sides of a right triangle. You will be able to compute the six ratios without a calculator for isosceles right triangles and 30° – 60° – 90° triangles. They will be able to apply the ratios to solve problems that can be modeled geometrically with right triangles, including "solving" right triangles.
 * Key Ideas**
 * 30°60° – 90° triangle || Secant (sec) ||
 * 45° – 45° – 90° triangle || Similar triangles ||
 * Cosecant (csc) || Sine (sin) ||
 * Cosine (cos) || Solving a triangle ||
 * Cotangent (cot) || Standard position of an angle ||
 * Right triangle trigonometry || Tangent (tan) ||

**Objectives**
You will understand how the trigonometric functions are extended by the unit circle to become functions of any angle. You will be able to use reference triangles to find trigonometric functions of real numbers.
 * Key Ideas**
 * Measure of an angle || Reference triangle ||
 * Initial side of an angle || Quadrantal angle ||
 * Terminal side of an angle || Unit circle ||
 * Positive and negative angles || Periodic function ||
 * Standard position of an angle || Period of a function ||
 * Coterminal angles || Circular functions ||

**Objectives**
You will be able to generate the graphs of the sine and cosine functions and explore various transformations of these graphs, called sinusoids, algebraically and geometrically. They will be able to model periodic behavior with sinusoids and thereby solve real-world problems.
 * Key Ideas**
 * Amplitude of a sinusoid || Phase shift of a sinusoid ||
 * Period of a sinusoid || Sinusoid ||

**Objectives**
You will be able to generate the graphs of the tangent, cotangent, secant, and cosecant functions and explore various transformations of these graphs.
 * Key Ideas**
 * Cosecant function || Secant function ||
 * Cotangent function || Tangent function ||

**Objectives**
You will be able to generate the graphs of sums, differences, and other composite functions that involve trigonometric functions. You will be able to model damped oscillation with a composite trigonometric function.
 * Key Ideas**

Damped oscillation Damping factor

**Objectives**
Students will be able to analyze the properties of the inverse trigonometric functions by deriving them from the corresponding properties of the trigonometric functions. Students will be able to produce the graphs of and simplify expressions involving compositions of trigonometric and inverse trigonometric functions.
 * Key Ideas** Inverse

cosine function (arccosine) Inverse sine function (arcsine) Inverse tangent function (arctangent)

**Objectives**
You will be able to model real-world problems with trigonometric functions and thereby solve them. Angle of elevation Angle of depression Simple harmonic motion
 * Key Ideas**