Branch of mathematics that studies the relationship between side length and angles of triangles
Widely used in the field of science
Circular Functions
Any amount of rotation generated when a ray is rotated about it’s endpoint
If the arrow is going clockwise it is a negative angle and if it is going counter-clockwise it is a positive angle
Angle
An angle positioned at (0,0) and has an initial side that is alone the positive side of the x-axis
Angles in standard position
A standard angle where the terminal side is on the x or y axis
Quadrantal Angle
Angles that are both in standard position and have the same terminal side
To get a coterminal angle add 360°
Ex. 42° = 42° + 360° = 402° = coterminal angle now :)
Coterminal Angles
Positive angles formed by the terminal side of the given angle and the x-axis
Are acute angles so should be less then or equal to 90°
How to get reference angles in every quadrant
Q1= same
Q2 =180° - θ
Q3= θ - 180°
Q4 = 360° - θ
Reference angles
On a circle of radius ® a central angle(θ) intercepts (s) through the formula of
S = rθ
Central Angle
A sector of a circle is the part of the interior of the circle cut by a central angle whose area A is given by the formula:
A = ½ θr2 , where θ is expressed in rad
Area of a sector
A circle whose center is at the origin and with a radius of 1 unit and every point on the circle satisfies x2 + y2 = 1
If:
x2 + y2 >1 then the point is outside the circle
x2 + y2 = 1 then the point is on the circle
x2 + y2 <1 then the point inside the circle
UNIT CIRCLE
A set of all points in a plane that are equidistant from a fixed point
Circle
(x-h)2 + (y+-k)2 = r2
Center Radius form
An equation that is true for all values of the variables for which every term of the equation is true (ex. 2x + 3x =5x)
Identity
An equation that is true only for some values of the variables for which every term of the equation is defined (ex. x + 3 = 5)
Conditional Equation
