AP Pre-Cal: 4.1 - 4.3 Notes BR

any three numbers that satisfy the pythagorean theorem

pythagorean triples

the ratio of the length of the sides from the corresponding

trig function

the measure of an angle where vertex is the center of the circle and intercepts an arc equal in length to the radius of the circle

radian measure

smallest possible angle that can be drawn from the terminal side and the x-axis

reference angle

quadrantal angles

if the terminal side of an angle falls on the x-axis or the y-axis, then that angle is called _____________. ________________

coterminal angles

angles that have the same initial and terminal sides are called ______________ ______________. Notice that these differ by 360

positive angles; clockwise rotations

_______________ ____________ are generated by counterclockwise rotation and negative angles are generated by ________________ ____________

degrees; radians

angles may be measured in either ______________ or ______________

positive; standard position

when the vertex of the angle is fixed at the origin of the coordinate plane with the initial side sitting on the _______________ x-axis, the angle is said to be in _______________ ______________

vertex

the endpoints of the ray is called the. _________________ of the angle

three; sides; measurement

the word trigonometry is derived from the Greek words “tri” which means ______________ “gonya” which means ______________, and “metron” which means _____________

geometry

trigonometry is a branch of _______________

initial; terminal

the starting position of the ray is the __________ side of the angle, and after rotatiion is the ____________ side

the rotation of an initial ray to a terminal ray about its endpoints

angle

Hipparchus; Father of Trig

____________ - 160 BC - known as _______________

triangle measurement

trignonometry literally means _________________

1,1,sqrt2 - 3,4,5 - 5,12,13 - 7,24,25 - 8,15,17 - 9,40,41

common triples

x, x, x sqrt3 - sin 60=sqrt/3 - cos 60=1/2 - tan 60=sqrt3

30 - 60 -90 triangle; give triangke measures then the 60 degree answers

x, 2x, xsqrt3 - sin 30=1/2 - cos 30=sqrt3/2 - tan 30=sqrt3/3

30 60 90 triangles - give triangle measures then give sin.tan.cos measures