Download Warm-up - mathew1

Warm-up:
1. How many degrees are in a circle?
2. What is the measure of the following angle?
3. Estimate the measure of the following angle.
1
Unlike in Geometry, in Precalculus we can have
negative angles as an indicator of direction.
Also, unlike in Geometry, in Precalculus we will
be measuring angles in degrees and...
__________
Like Celsius and Fahrenheit measure
temperature, degrees and ________ measure
angles.
2
Conversions between Degrees and Radians
o
Use the basic relationship π rad = ____ .
1. To convert degrees to radians,
multiply the degree by _______ .
2. To convert radians to degrees,
multiply the radian by ________ .
3
Convert from radians to degrees.
1. 9π/2
2. -π/2
3. 2
Convert from degrees to radians.
4. 1350
5. 5400
6. -3120
4
_____
5
Complete the following using degree measures.
1. An angle is acute if its measure is between
________ and ________.
2. An angle is obtuse if its measure is between
________ and ________.
3. Two angles are complementary if the sum of
their measures is ________.
4. Two angles are supplementary if the sum of
their measures is ________.
6
Remembering what you know about angles in
degree measure, complete the following using the
equivalent radian measures.
An angle is acute if its measure is between
________ and ________.
An angle is obtuse if its measure is between
________ and ________.
Two angles are complementary if the sum of
their measures is ________.
Two angles are supplementary if the sum of
their measures is ________.
7
Complements and Supplements
0
Complementary angles- their sum is __ ( ___ )
0
Supplementary angles- their sum is ___ ( __ )
To find the complement of an angle, subtract from __
if in degrees or subtract from ____ if in radians.
0
0
* angles bigger than 90 (π/2) cannot have complements.
To find the supplement of an angle, subtract from
___ if in degrees or subtract from __ if in radians.
0
0
* angles bigger than 180 (π) cannot have supplements.
***Complements and supplements can never be negative.
8
Classify as acute, right, obtuse, or neither. Then
determine the complement and the supplement.
Type of Angle Complement Supplement
1. 2π/5
2. 4π/5
3. 49
0
4. 7π
6
9
Quadrants
0
θ = __ , ___
Quadrant I
Quadrant II
0
0
0
0
__ < θ < ___
__ < θ < __
___ < θ < __
__ < θ < ___
0
0
θ = __ , __ θ = ___ , __
__ < θ < ____
0
____ < θ < __
0
0
0
___ < θ < ___
___ < θ < ___
Quadrant III
Quadrant IV
0
θ = ___ , ___ 10
Tell which quadrant each angle is in and
Sketch each angle in standard position.
1. 68
0
3. ­126
2. π/4
0
5. ­5π/6
4. 5π/3
6. 4
11
Two angles are ________ if they have the same
initial and terminal side.
300
In radians, you can find coterminal angles by adding
or subtracting multiples of ____.
In degrees, you can find coterminal angles by adding
or subtracting _____.
0
12
Determine two (one pos. and one neg.) coterminal
angles for each angle.
Positive
Negative
0
1. 62
2. 6π/5
3. ­214
0
4. 23π/12
13
Homework:
pg. 291
#s 5,6,8,16,17,19,
35,40,43,46,56,57
14