Ch 4 Trig Functions. 4.1 Radian and Degree Measures Converting from Radians to Degrees Converting...
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Transcript of Ch 4 Trig Functions. 4.1 Radian and Degree Measures Converting from Radians to Degrees Converting...
![Page 1: Ch 4 Trig Functions. 4.1 Radian and Degree Measures Converting from Radians to Degrees Converting from Degrees to Radians.](https://reader036.fdocuments.in/reader036/viewer/2022081506/56649ef05503460f94c008fa/html5/thumbnails/1.jpg)
Ch 4 Trig Functions
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4.1 Radian and Degree Measures
Converting from Radians to Degrees
Converting from Degrees to Radians
180
radiansdegrees
180
degreesradians
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4.1 Angles in Standard Position
vertex at origin initial side
on positive x-axis
terminal sidecounter-clockwise from initial side
40
50complement
140supplement
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4.1 Arc Length
240
rs length arcs
radiansin angle
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4.1 Arc Length
rs
Find the length of the arc intercepted by a central angle of 45o in a circle with a radius of 10cm.
410
cms
cms2
5
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4.1 Linear and Angular Speed
240
time
angle centralspeedAngular
time
length arcspeedLinear
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4.1 degrees, minutes, seconds
Converting minutes and seconds to degrees.
Converting decimal degrees to minutes and seconds.
3600
seconds
60
minutes + degrees = degrees
'8.2535
'6043.3543.35
"608.0'2535
"48'2535
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4.2 Unit Circle
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4.4 All Students Take Calculus
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4.4 Evaluating Trig Functions of Any Angle
Given and , find and .4
5tan
4145 22 r
41
41
415sin
0cos secsin
tan (-) and cos (+) = QIV
Draw angle from origin to x-axis.-5
4
4
41
cos
1sec
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4.4 Reference Angle
Angle to x-axis.
' '
' 2'
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4.5 Graphs of Sine and Cosine Functions
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4.5 Graphs of Sine and Cosine Functions
bxaybxay cosor sin
aamplitude
xy 2cos3Find the amplitude and period.
b
π2period
3amplitude period
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4.5 Graphs of Sine and Cosine Functions
cbxaky sin
kShift Vertical
a
c Shift Horizontal
Vertical and Horizontal Shifts
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4.7 Inverse Trig Functions
h
osin
h
oarcsin
Take the sin of an angle to get a ratio
Take the arcsin of a ratio to get an angle
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4.7 Inverse Trig Functions
5
3arcsincos
5
4cos
Find the exact value.
-35
4
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5.1 Identities
Pythagorean Identities Quotient Identities
sin2 cos2 1
1 tan2 sec21 cot2 csc2
x
xx
cos
sintan
x
xx
sin
coscot
Be familiar with identities on the inside of front and back cover of book (on blue cheat sheet).
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6.1 Law of Sines
The ratios of angles and corresponding sides are equal.
C
c
B
b
A
a
sinsinsin
A
b
12c73B
a
80CFind b.
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6.2 Law of Cosines
Abccba cos222
A
b
12c73B
9a
CFind b.
bc
acbA
2cos
222
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6.3 Vectors
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VectorsA vector whose initial point is at the origin is in standard position.
The magnitude of a vector is its length.
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Vectors
The magnitude (length) of v
v x2 x1 2 y2 y1 2
initial point P x1,y1
terminal point Q x2,y2
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VectorsThe components (direction) of v
one unit to the lefttwo units up
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Scalar Multiplication of VectorsVectors can be multiplied to change its scale.
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Vectors AdditionVectors can be added.
=commutative
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Addition of Vectors
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The Unit VectorTo get a unit vector, divide the vector by its magnitude.
u = unit vector
vv
or 1v
v
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i and jhorizontal and vertical components
horizontal component ivertical components j
v =
2,4 2i 4 j
v1,v2 v1 v2v = i j
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The Unit VectorWrite a vector as a combination of unit vectors.
i represents a horizontal unit vectorj represents a vertical unit vector
i i ijj
jj
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Unit Vectors on Unit Circleu
x,y cos, sin
cosi sinj
Find the magnitude and direction angle of the vector.
v 9 cos30 i sin 30 j
v 9
30