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Transcript
Coterminal Angles, Unit
Circle
Chapter 2
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Coterminal Angles
Find 3 angles coterminal to the following:
a) 34°
a) 123°
b) -279°
c) -106°
Coterminal Angles
Find the smallest posititve angle coterminal to
the following:
a) 623°
a) 1023°
b) -279°
c) -106°
Given the initial position of the dial is at
zero, how many degrees is the dial rotated
in total(sum of clockwise and
counterclockwise rotations) to open the
lock if the combination is 20-15-5
1665°
Trigonometric Values
Find the 6 trig function values at the point (2,-7)
Trigonometric Values
 Find all 6 trig function values given the equation
3x-y = 0, x>0
Start out by choosing a convenient value for x.
Trigonometric Values
 Find all 6 trig function values given the following
equations:
a) 2x-5y = 0, x<0
b) 3x+7y =0, x>0
Trigonometric Values
 Find all 6 trig function values at 30°
Trigonometric Values
 Find all 6 trig function values at 30°
Trigonometric Values
 Find all 6 trig function values at 45°
Trigonometric Values
 Find all 6 trig function values at 45°
Quadrants
Quadrants
Quadrants
Quadrants
These function are always positive in these quadrants.
Quadrants
A better way to remember which functions are positive.
Seniors
Take
Civics
Find all 6 trig function values given
Cosθ=-5/13 in Quadrant II
Find all 6 trig function values with the given information.
a) Sinθ= 3/5 in QII
b) Cosθ= ¼ in QIV
c) Secθ= 5/3 in QI
d) Cotθ= 7/3 in QIII
TEAMS
P 50……..#’s 4,6,8,16,18
Cofunctions
Cofunctions
 Find the cofunction for Sin 43°
Find the value of each cofunction.
a) Sin 72°
b) Csc 24°
c) Cot 71°
d) Cos(θ – 42°)
True or False
 Is Cos 32° < Sin 56°
From 0° to 90°
Sin,Sec,Tan Increase
Cos90° = 0
Sin90° =1
Cos0° = 1
Sin0° =0
Cos,Csc,Cot Decrease
True or False
 Determine whether the following are True or False?
A) Sin 43° > Cos 29°
B) Cot 21° < Tan 82°
C) Sec 73° > Csc 27°
TEAMS
Unit Circle
These are the angles we care about most in Trigonometry.
Unit Circle
Unit Circle
Unit Circle
Unit Circle
Find all 6 trig function values at 60
degrees.
Find all 6 trig function values at 90
degrees.
Reference Angles
Find all 6 trigonometric function values at 240 degrees.
Reference Angles
Find all 6 trigonometric function values at each of the
following angles.
a) 180°
b) 300°
c) 135°
Find your reference angle first!
Negative Angle Measures
Find all 6 trigonometric function values at -120 degrees.
Negative Angle Measures
Find all 6 trigonometric function values at -30 degrees.
Coterminal Angle Measures
Find all 6 trigonometric function values at 1020 degrees.
Trigonmetric Functions
 Find all 6 trig functions at the given angle. Find the reference
angle, draw the angle
a) 315°
b) -135°
c) -270°
d) 510°
e) -300°
Trigonmetric Functions
Trigonmetric Functions
TEAMS
P 88……#’s 12,14,24,26,30
Evaluate the following
cos60° + 2sin230°
Evaluate the following
a) tan2120° – 2cot240°
b) Sec2300° - 2cos2150° + tan45°
c) 3tan135° + 4cos(-180°) – 2csc270°
Evaluate the following
a) cot45° – 2sec300°
b) sec2300° - 2sin2150° + tan(-45°)
c) 3tan135° + 4sec(-180°) – 2cos270°
d) sin300° - 2sin240° + sin2(-120°)
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