Transcript Cofunctions, Unit Circle

Cofunctions, Unit Circle
#2
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
P 68……#’s 10,12,18,24,28
Unit Circle
These are the angles we care about most in Trigonometry.
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°
Solving Right Triangles
Solving Right Triangles
Solving Right Triangles
Solving Right Triangles
12
Solving Right Triangles
A
12.2
C
19.3
B
Solving Right Triangles
A
16
9
C
B
Solving Right Triangles
A
12.4
C
18.3
B
Solving Right Triangles
A
65° 41’
5.92
C
B
Solving Right Triangles
A
19
32° 23’ 29”
C
B
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° + 4csc(-180°) – 2cos270°
d) sin300° - 2sin240° + sin2(-120°)
Special Right Triangles
Special Right Triangles
Special Right Triangles
Special Right Triangles