Name: ____________________ Pre- Calculus 12 H Date: _____________

Chapter 4– Trigonometry & the Unit Circle Section 4.1 B – Standard and Co-terminal Angles

To study angles with respect to the Cartesian coordinate system, we must first agree on a set way to place an

angle in the coordinate plane. We say that an angle

is in standard position in the coordinate plane if the

following two requirements are satisfied.

a) The vertex of the angle

is at the origin.

b) The initial side of

lies on the positive x–axis.

When the vertex of an angle is positioned at the origin and the initial ray lies along the positive x -axis, the

angle is said to be in standard position.

Example 1: Sketch the following angles in standard position

a) 120o

and -50o b)

6

red and

5

4

rad

The circle below is divided by lines with different angles. The lines are called __________________.

Label the angles in both degrees and radians.

Angles can go around the circle more than once before stopping on the same terminal.

We call these angles___________________________

Co-terminal angles are angles in standard position that share the same terminal arm. They can be found

by adding or subtracting multiples of 360o (in degree) or 2 (in radian).

Every angle in standard position has an infinite number of co-terminal angles associated with it.

Co-terminal angle

In degree: In radian:

________________________ ________________________

Example 2: Graph each angle below. Then write a general equation to express its co-terminal angle.

a) = 210o b) =

6

Example 3: Given2

, find all angles that are coterminal in the domain 2 4 .

Example 4: Find an angle with measure between 0◦and 360

◦ that is co-terminal with the angle of measure

1290◦ in standard position.

Example 5: Determine all angles, , conterminal with angle 5

6

that satisfy the domain 4 4

Example 6:

(a) Find an angle between 0 and 2 that is co-terminal with 100.

(b) Find an angle between 0◦and 360

◦ that is co-terminal with -3624

◦.

Assignment: p. 175 #6-11