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Trigonometry
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Gravity
Key Concepts:
Terms in this set (31)
Complementary Angles
either of two angles whose sum is 90°.
Supplementary Angles
either of two angles whose sum is 180°.
Standard Position
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Quadrantal Angle
An angle with terminal side on the x-axis or y-axis. That is, the angles 0°, 90°, 180°, 270°, 360°
Coterminal Angles
angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal.
Radian
a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.
2pi radians in degrees?
360 degrees
Circumference of a circle?
2 Pi Radius (or radians)
Convert 180 deg to radians
pi
Convert 90 deg to radians
1/2 pi
Convert 45 deg to radians
pi/4
Convert 30 deg to radians
pi/6
Convert 60 deg to radians
pi/3
What is the arc length formula
Arc Length= (θ/360)2πr A circle is 360° all the way around; therefore, if you divide an arc's degree measure by 360°, you find the fraction of the circle's circumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle's circumference) by that fraction, you get the length along the arc.
Area of a sector and formula in degrees
(θ/360)πr^2 The portion of the interior of a circle intercepted by a central angle. Like a piece of pie.
Linear speed
As a point moves along a circle of a radius, r, its angular speed, ω, is the angular rotation per unit time, t ω(angular speed in radians/sec)= θangle in radians (2π radians = 360 degrees)/time
Velocity
Velocity= Distance/Time v=s/t
Angular Speed
A measure of how fast a central angle is changing,Angular speed is the rate at which an object changes its angle (measured) in radians, in a given time period. Angular speed has a magnitude (a value) only.
Angular speed = (final angle) - (initial angle) / time = change in position/time
ω = θ /t
ω = angular speed in radians/sec
θ = angle in radians (2π radians = 360 degrees)
t = time, sec
Angular speed and angular velocity use the same formula; the difference between the two is that Angular speed is a scalar quantity, while angular velocity is a vector quantity.
sin θ
y/radius
csc θ
r/y
cos θ
x/r
sec θ
r/x
tan θ
y/x
cot θ
x/y
soh cah toa
sin= opposite/hypotenuse cos= adjacent/hypotenuse tangent= opposite/adjacent
Sine and Cosine Function on the Unit Circle
If t is a real number and a point (x,y) on the unit circle corresponds to an angle of t, then
cos (t)=x
sin (t)=y
cos (t)=?
x-coordinate
sin (t)
y- coordinate
tanget=
y coordinate/x coordinate
Pythagorean Identity
because of the pythagoream theoreom and a^2 = sin theta, b^2= cos theta, and c^2=1^2. you can see why this formula is true on a unit circle with a radius of 1.
30 60 90 triangle
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