Download Trigonometry 1 - Angles in Standard Position

Math 20-1
Trigonometry Lesson #1
Angles in Standard Position
Objective: By the end of this lesson, you will be able to:
- Sketch an angle in standard position, given the measure of the angle between 0° and 360°
or a point on the terminal arm
- Determine the quadrant in which an angle in standard position terminates
- Determine the reference angle of an angle in standard position
An angle is in standard position when its vertex is on the ____________ and its initial arm is on
the ______________ ___________. The other arm of the angle is called the ________________
________. The angle is measured in a _______________________________ direction.
A common variable for angles is  , the Greek letter theta.
Recall: Quadrants of the Cartesian Plane
Label the Quadrants I, II, III, and IV on the Cartesian plane. Then label the degree measurements
of each axis.
The angles drawn above whose terminal arm lies on the x- or y-axis are called _______________
angles.
Math 20-1
Trigonometry Lesson #1
e.g. 1) Use a protractor to sketch each angle in standard position. In which quadrant does the
terminal arm of each of the following angles terminate?
a) 127
b) 340
c) 270
How did you measure the angle 340 in part b?
Reference Angles
Angles in standard position can be _____________ ( 0    90 ), _____________
( 90    180 ), or _____________ ( 180    360 ). However, every angle in standard
position has a corresponding acute angle called the ___________________ ____________. The
reference angle is the acute angle between the terminal arm and the _____________. The
symbol ______ is used for the reference angle.
e.g. 2) Determine the reference angle for each of the angles in e.g. 1).
a) 127
b) 340
c) 270
Summary:
Quadrant I
R 
Quadrant II
R 
Quadrant III
R 
Quadrant IV
R 
e.g. 3) Determine the reference angle for 146 . Then write three other angles in standard
position that have the same reference angle. Indicate which quadrant each angle is in.
Math 20-1
Trigonometry Lesson #1
An angle in standard position can also be defined by a point on its terminal arm.
e.g. 4) Sketch an angle in standard position whose terminal arm passes through each of the
following points. Then state in which range ( 0    90 , 90    180 ,
180    270 , or 270    360 ) the measure of the angle is.
a) (1, -5)
b) (-4, -3)
e.g. 5) a) Draw the angle in standard position that passes through the point (6, 4).
b) Write a point on the terminal arm of the angles in the other three quadrants that have
the same reference angle as the one drawn above. Then sketch each angle on the grid
above.
Summary:
The point (x, y) has the same reference angle as the points _________, __________, and
_________.
Assignment:
p. 83-86 #1-7, 9, 12, 14
p. 96 #1
For a challenge: p. 85-86 #16, 19