20 Days
Three days

One radian is the measure of the central
angle of a circle subtended by an arc of equal
length to the radius of the circle.
1. 180   radians
2. 1 

180
radians  0.0175 radians
3. 1 radian 
180

 57.2958
To Change From :
Multiply by :
Example :
Degrees to Radians
  


 180 
   2
120  120

 180  3
Radians to Degrees
 180 


  
4 4  180 


  240
3
3   
A circle with radius of 1
Equation x2 + y2 = 1
0,1
 1,0

0,1
cos , sin  
1,0

Read 5.1 and Complete "What do you know
about Trig" WS





Angle – Set of points determined by two rays.
Example <AOB
In trig, we often think of angles as the rotation
of rays. This gives us some new vocab.
Initial side – the fixed ray from which we
measure an angle.
Terminal side – the rotated ray that
determines the measure of an angle.
Vertex – the point about which the terminal
side is rotated and is common to both sides.



Coterminal angles - two angles with the same
initial and terminal sides.
Straight angle – an angle whose sides line on
a straight line and extend in opposite
directions from the vertex.
Degrees – One unit of measuring an angle.
One complete revolution in the counter
clockwise direction is 360*.



Using the x-y plane, the standard position of
an angle has its vertex at the origin and its
initial side as the positive x-axis.
If the terminal angle is rotated counter
clockwise, the angle is positive.
If the terminal angle is rotated clockwise, the
angle is negative.
If   45 is in standard position, find two positive
and two negative angles that are coterminal with  .

You should be familiar with the following terms:
Right angle 
Acute angle 
Obtuse angle 
Compliment ary angles  , 
Supplement ary angles  , 
  90
0    90
90    180
    90
    180
If an arc of length s on a circle of radius r subtends
a central angle of radian measure  , then
s  r
Given a circle with radius r  4cm and  
find the arc length s.

6
,
Given s  12 and   7, find the radius r.
Given s  3cm and r  5, find  in radians.
If  is the radian measure of a central angle of a circle
with radius r and if A is the area of the circular sector
determined by  , then
1 2
A r 
2


p359 (#1,3,9 - 11,13,15,16,29, 31a, 33a)
Read p349 - 351, 353(note blue box and
below), 354 and example 5

When more precise measurements are
required, we can extend our measurement to
more decimal places, or we can divide the
degree into equal parts called minutes
(denoted ‘) and seconds (denoted “).
Thus, 1  60' and 1'  60".
  2914'45" refers to the angle that has measure
29 degrees, 14 minutes, and 45 seconds.
Find the angle that is complement ary to  .
a.)   2914'45"
b.)   81.34
If   4, approximat e  in terms of degrees, minutes,
and seconds.

p359 (#4,6,12,14,21,24,25,28,30,32,35-37,39)
Four Days

We can refer to the three sides of any right
triangle in relation to a specific acute angle as
the adjacent, opposite, and hypotenuse sides.

The six trig functions are the sine, cosine,
tangent, cosecant, secant, and cotangent.
opp
sin  
hyp
1
hyp
csc  

sin  opp
adj
cos  
hyp
1
hyp
sec  

cos  adj
opp
tan  
adj
1
adj
cot  

tan  opp
cos
tan

Find the six trig values for θ in the triangle
4
below.
sin   5
3
cos   5
5
tan   4
4
3
csc   5
3
4
sec   5
3
cot   3
4

Find the six trig values for θ in the triangle
below.
sin   24  12
cos  
4
2

3
2
2

1
3
tan   2 3
csc  
2 3
2 3
4
4
2
2
4
sec   2 3
cot  
2 3
2

2
3
 3

Find the six trig values for θ if θ is in
standard position and P(2,-5) is on the
terminal side.
sin   2
29
cos  
5
29
tan  
2
5

29
5
2
P (2,5)
csc  
29
2
sec   
29
5
cot  
5
2

Find the values of x and y in the triangle
below using trig functions.
6
x 3
 30
y 3 3
y
x
cos(30) 
sin( 30) 
6
6
x  6 sin( 30) y  6 cos(30)
y  6 23
x  6 12 
 
x3
y3 3
You are visiting
Sequoia National
Park in California to
see the Giant
Redwood Trees.
You are standing
500ft away from the
biggest tree that you
can find and the
angle between the
ground and the top
of the tree is 33*.
How tall is the tree?


p375 (#2,3,9, 11, 21,22,24,27—exact
answers until #21)
Read p362 - 365

Find the six trig values for θ if θ is in
standard position and is on the line y=-4x.

4
1
17
y  4 x
sin  
2
29
cos  
5
29
tan  
2
5
csc  
29
2
sec   
29
5
cot  
5
2

Given that tan  
values.
11
5
find the remaining trig
sin  
cos  
tan  
csc  
sec  
cot  
cos
tan

Recall that the unit circle has its center at (0,0) and a
radius of 1. If we divide the special right triangles so
the hypotenuse equals 1 we get that the points on
the unit circle have coordinates (cos  , sin  ) .
(cos  , sin  )

The the coordinates on the unit circle are of
the form (cos  , sin  ). We get the following
values for 0, 30, 45, 60, and 90 degrees.

You must memorize the following ASAP!!
Rad
Cos
Sin 
0
0
1
0
30

3
2
1
2
45

2
2
2
2
60

1
2
3
2
90

0
1
Deg
6
4
3
2

p375 (#4,12 ̶ 18 even, 28, 67,70,74,78)

We can see that the 6 trig functions are
reciprocals of one another. Sin and Csc are
reciprocals, Cos and Sec are reciprocals, and
Tan and Cot are also reciprocals.
1
sin  
csc 
1
cos  
sec 
1
tan  
cot 
1
csc  
sin 
1
sec  
cos 
1
cot  
tan 
RECIPROCAL IDENTITIES
1
csc 
sin 
1
sec  
cos 
1
cot  
tan 
QUOTIENT IDENTITIES
cos 
sin 
cot  
tan  
sin 
cos 
PYTHAGOREAN IDENTITIES
sin   cos   1
2
2
tan   1  sec 
2
2
1  cot 2   csc 2
All of the identities we learned are found in the back page of your
book under the heading Trigonometric Identities and then
Fundamental Identities.
You'll need to have these memorized or be able to derive them for this
course.

We can verify that the following identity is true
by making the left side match the right side.
sin 
tan  
cos 

Deriving the Pythagorean Identity using the
Pythagorean Theorem and the unit circle.
x2  y 2  1

When verifying identities, it is important to
remember that all 6 trig functions can be
written using sin and/or cos.
sin   sin 
cos   cos 
1
csc  
sin 
1
sec  
cos 
sin 
tan  
cos 
cos 
cot  
sin 

Verify the following identity by re-writing the
left hand side to match the right hand side.
tan  cot   1
sin  cot   cos

Verify the following identity by re-writing the
left hand side to match the right hand side.
sin   cos 
 1  tan 
cos 

Verify the following identity by re-writing the
left hand side to match the right hand side.
cos 2 2  sin 2 2  2 cos 2 2  1

worksheet 5.1 & 5.2 problems

Pg 377 (# 50,54,57,58,59)


As a class, we are going to do the following
problems on the board. Volunteers?
p375 #10,13,15,17

p377 (#45 ̶ 53 odd, 57)

A ladder leaning against the wall makes an
angle of 80* with the ground. If the foot of
the ladder is 6ft from the wall, how high is
the ladder?

Your line of sight to the top of a mountain
makes a 34* angle with the horizontal. If the
line of sight is measured at 5500ft, how tall is
the mountain?

A boy flying a kite lets out 400ft of string
which makes an angle of 42* with the
ground. Assuming the string is straight and
the ground is level, how high above the
ground is the kite?

A wire is attached to the top of a flagpole and
is staked to the ground 30ft from its base. If
the wire makes a 64* angle with the ground,
how tall is the flagpole?

An airplane climbs at a 9* angle after takeoff.
How far has the plane traveled horizontally
when it has attained an altitude of 3000ft?

p377 (#29, 68,69,71,73,77,80, 81,83 #81 &
83)
Four Days
sin( t )   sin t cos( t )  cos t
csc( t )   csc t sec( t )  sec t
sin  4  
cos 56  
tan( t )   tan t
cot (t )   cot t

Applications #1 worksheet

p394 (#3,9,12,15,19 - 21, 24,25)

A reference angle is an acute, positive angle
formed between the terminal side and the xaxis.

Sine and Cosine are periodic functions, that is
there exists a positive real number k such
that f(t+k)=f(t) for every t in the domain of f.
sin   2n   sin  
cos  2n   cos 


This video graphs all three functions
simultaneously while rotating the angle in
standard position on the unit circle.
http://www.dnatube.com/video/12168/Triggraphs

http://www.touchmathematics.org/topics/tri
gonometry
Even Functions
Odd Functions
f ( x)  f ( x)
f ( x)   f ( x)
cos    cos 
sin      sin  
sec    sec 
csc     csc 
tan      tan  
cot      cot  

Given a trig value, find θ.
sin  
cos  
  6 , 56 , 136 , 76
1
2
3
2
  6 , 116 , 136 , 6
tan   1
  4 , 4 , 54 , 4
sin  

 2
2

4
, 54 , 74 , 4

Review 5.1 - 5.3 worksheet

Find the angle(s) that satisfies each equation:
sin  
 2
2
cos   1
tan   3
csc   2
sin   .834
cos   .6
tan   1.76
tan   21
cos   2

Applications worksheet 2 (#1 - 3, 5 – 7)


A drawbridge is 150ft long across a river.
The two sections are of equal length and can
be rotated upward to an angle of 35*.
If the water level is 15 feet below the bridge
when it is closed. Find the distance between
the end of each section of the bridge when
raised and the surface of the water.

A plane is on approach to the Harrisburg
Airport at a current elevation of 10000ft. If
the plane is 12 miles away what angle of
decent should the pilot take to land at the
airport?

Find the height of the Matterhorn.

Find the distance to the island.
Three Days

A reference angle is an acute, positive angle
formed between the terminal side and the xaxis.

p404 (#2,3,8 - 18 even(w/out a calculator),
19,21,25,29,33,43)



Reference angle worksheet
Finish Applications paper #8 plus
p405 #36

Applications #3 worksheet
Two Days

p436 (#3,6,11,14,25,27,29,34 exact answers
for #3 & 6, look at diagram for 25,29,34)

p442 (#1 - 4, 7,8,21 - 24, 27,30, 67, 68)


Prentice Hall p21 (#3,15,16,19,20,25)
No calculator