unit recap 6

Max, min, domain, range, intercepts

x g(x) Page 6 graph functions, domain, range, max, minimum, vertex, xyintercept.notebook 6 September 26, 2014 Use a function table to graph the following functions. List the Domain, Range, x-intercept and y-intercept, minimum or maximum and vertex.

Circles

A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

Radians

Converting radians to degrees: To convert radians to degrees, we make use of the fact that p radians equals one half circle, or 180º. This means that if we divide radians by p, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees.

radian

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30 , − and 390 are all coterminal.

(cosine = x coordinate and sine = y coordinate)

In conclusion, the reason that the sine function, sin θ, corresponds to the y coordinate, and the cosine function, cos θ, corresponds to the x coordinate is by definition; This fact is especially evident when using the special case of the unit circle (r = 1) to express those definitions.

Use the Unit Circle to derive functions for sine and cosine

Sine and Cosine Functions. If t is a real number and a point (x, y) on the unit circle corresponds to an angle of t, then. (5.6) cos t = x. (5.7) sin t = y. Given a point P (x, y) on the unit circle corresponding to an .... calculate sines and cosines of the special angles using the Pythagorean Identity and our knowledge of triangles.

Area of a Circle and Arc Length

So the arc is a quarter of the circumference, and the sector area is a quarter of the area of the circle. And the sector area is 2/5 of the area of the circle. Work out the length of each arc and area of each sector to 3 decimal places (d.p.) Arc length = 1/5 of 10 π = 2 π = 6.283cm (3 d.p.)

Radians

The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

Constructing the unit circle using special right triangles

This article explains an easy way to memorize points on the unit circle. Unit Circle with Radians. Next, we will define the X and Y Coordinate points on the Unit Circle. In order to do this, we need to understand the relationship of the Special Right Triangles 30 - 60 - 90 and 45 - 45 - 90 degrees to the coordinate plane.

Amplitude

Time-saving video on wave amplitude. Wave amplitude measures how far a wave rises and falls and is one of four main wave characteristics found in Physics. Video explanation on amplitude and example problems.

Period

a length or portion of time.

Midline

a median line or plane of bilateral symmetry, especially that of the body.

Unit Circle

In mathematics, a unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

e and sine = y coordinate) • Graphs of Sine and Cosine

Like all functions, the sine function has an input and an output. Its input is the measure of the angle; its output is the y-coordinate of the corresponding point on the unit circle. The cosine function of an angle t equals the x-value of the endpoint on the unit circle of an arc of length t.

Trig Ratios and Reciprocal Identities

Search Results Relationship between sine / cosine / tangent and cosecant / secant / cotangent. You are already familiar with the trig identities of sine, cosine, and tangent. As you know, any fraction also has an inverse, which is found by reversing the positions of the numerator and denominator