precalc unit 4 trig...
TRANSCRIPT
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 1610:05 PM
Bell Ringer
30
60
30
60
If you shrink a 30, 60 ,90 triangle so that its hypotenuse is 1, what are the lengths of the other 2 sides?
What is sin (30) in the smaller triangle?
2 1
√3
Dec 169:32 PM
So...... if get a circle has a radius of 1, then the hypotenuse be 1:
1
Then the sin will just be opp (or y value)
and the cos will just be adj (or x value)
we call this a
UNIT circle
(because the
radius is 1 unit)
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Jul 2611:53 AM
4.3 Trigonometric Functions &
the Unit Circle
Lesson Objectives:
1) I can find values of trig functions for any angle
2) I can find values of trig functions using the unit circle
Dec 169:32 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 169:56 PM
Then we can get values for the Quadrantal Angles:
Find the exact value of each trig function, if defined. Write undefined if not defined.
sin (180°) tan
cos (270°) csc π/2
cot (90°) sec 4π
Dec 169:59 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 169:58 PM
So what about tangent?
sin Θ
cos Θ
1
well, if
tan Θ = opp
adj
then
tan Θ = sin Θ
cos Θ
Dec 169:58 PM
Then cotangent is just the reciprocal of tangent so
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 169:58 PM
GUIDED PRACTICEThe given point lies on the terminal side of an angle theta in standard position. Find the value of the 6 trig functions of theta.A) (4, 3) B) (2, 1)
TOO EASY! Let's crank it up!
C) (4, 3) D) (2, 1)
Dec 156:14 AM
Even when that 'else'
is neither an acute nor
a quadrantal angle.
Reference angles
are useful in
those instances
Sketch the angle. Then find its reference angle.
300 240 390 ° ° °
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 156:14 AM
OK, so knowing that, we can evaluate the trig functions of any angle. But, in which quadrant(s) are each of the trig functions positive or negative?
Dec 156:14 AM
We can use a pnemonic device:
AllStudents
Take Calculus
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 156:14 AM
Now you try it:Tan ( ) = -5/12 and sin ( ) < 0
Find the quadrant, all 6 trig ratios, and the value of angle .
II I
III IV
Dec 156:14 AM
Try One More:Cos ( ) = √3/2 and sin ( ) < 0
Find the quadrant, all 6 trig ratios, and the value of angle .
II I
III IV
PreCalc Unit 4 Trig Functions.notebook
8
November 20, 2018
Dec 156:14 AM
OK maybe just one More:csc ( ) = √2 and tan ( ) < 0
Find the quadrant, all 6 trig ratios, and the value of angle .
II I
III IV
Dec 169:58 PM
REAL WORLD APPLICATIONS (GUIDED PRACTICE)ROBOTICS As part of the range of motion category in a high school robotics competition, a student programmed a 20cm long robotic arm to pick up an object at point C and rotate through an angle of exactly 225° in order t release it into a container at point D. Find the position of the object at point D, relative to the pivot point O. ***HINT: DRAW yourself a picture****
CLOCKWORK A 3inchlong minute hand on a clock shows a time of 45 minutes past the hour. What is the new position of the end of the minute hand relative to the pivot point at 10 minutes past the next hour?
PreCalc Unit 4 Trig Functions.notebook
9
November 20, 2018
Dec 169:32 PM
So...... if get a circle has a radius of 1, then the hypotenuse be 1:
1
Then the sin will just be opp (or y value)
and the cos will just be adj (or x value)
we call this a
UNIT circle
(because the
radius is 1 unit)
Dec 169:59 PM
When defined asfunctions of the real #
system on a unit circle,
our 6 trig functions are
often called
circular functions
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 169:58 PM
Find the exact value of each expression (using the Unit Circle). If undefined, write undefined.
cos 135° tan 270° sin 120° cot 210°
sin csc cos sec
Dec 169:58 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Jan 610:59 PM
sin Θ is the y value on the circle and the height of the triangles
Jan 610:40 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Jan 610:40 PM
Jan 610:40 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Jan 610:59 PM
cos Θ is the x value on the circle and the width of the triangles
Jan 610:40 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Jan 610:40 PM
Jan 610:46 PM
PreCalc Unit 4 Trig Functions.notebook
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November 20, 2018
Dec 169:58 PM
Use your knowledge of the periodic nature of Circular Functions to find the exact value of each expression:
Cos Sin Tan
Sin Cos Tan
Nov 207:45 AM
HOMEWORK:PreCalc:pp. 251253, # 6, 9, 17, 25, 32, 42, 52, 55, 60, 63, 69, 73, 83, 103, 106
(HON)/Calc: pp. 580581, # 6, 14, 16, 19, 22, 28, 43, 44, 49, 51, 59, 60, 71