1
Algebra 3 Assignment Sheet
WELCOME TO TRIGONOMETRY, ENJOY YOUR STAY
(1) Assignment # 1  Complete the circle diagram
(2) Assignment # 2  Sine & Cosine functions chart
(3) Assignment # 3  Other Trig functions chart
(4) Assignment # 4  Finding other trig functions
(5) Assignment # 5  Review Worksheet
(6) TEST
(7) Assignment # 6  Angle Addition Formulas
(8) Assignment # 7  Double, Half-Angle Formulas
(9) Assignment # 8  Review Worksheet
(10) TEST
(11) Assignment # 9  Trig Identities (1)
(11) Assignment # 9  Trig Identities (2)
(12) Assignment # 10 Problems ( 1 – 9 )  Solving Trig Equations
(13) Assignment # 10 Problems ( 10 – 18 )  Solving Trig Equations
(14) Assignment # 11  Review Worksheet – Solving Trig Equations
(15) TEST
2
INTRODUCTION TO TRIGONOMETRY
I Definition of radian: Radians are an angular measurement. One radian is the measure of a
central angle of a circle that is subtended by an arc whose length is equal to the radius of the circle.
10
Therefore:
5
1
arc length = angle in radians x radius
2R
R
5
5
3
The radius wraps itself around the circle 2 times. Approx. 6.28 times.
Therefore 360 = 2 R
2 R
R
……….. 1 
360
180
180
………………………... 1R  R
1

2
6
Dividing you get 1 
Conversely
2

Ex. Change 60 to radians.
5
Change
0 , 2
R


4
4
R
to degrees.
3
2
Convert the following from degrees to radians or vice versa:
1. 36
2. 320
4.

15
5.
17
20
3. 195 0
6.
5
3
3
II UNIT CIRCLE:
The unit circle is the circle with radius = 1, center is located at the origin.
What is the equation of this circle?
Important Terms:
A. Initial side:
B. Terminal side:
C. Coterminal angles:
D. Reference angles:
The initial and terminal sides form an angle at the center
if the terminal side rotates CCW, the angle is positive
if the terminal side rotates CW, the angle is negative
unit circle
positive
negative
Coterminal angles have the same terminal side…. -45˚ and 315˚ or
coterminal

7
and
3
3
The reference angle is the acute angle made between the Terminal Side and the x-axis
4
III GEOMETRY REVIEW
30 – 60 – 90 
RIGHT TRIANGLES
45 – 45 - 90 
45 
60 
2a
a
a 2
a
45 
30 
a
a 3
Therefore, for the Unit Circle, hypotenuse is always 1.
45 
60 
1
1
2/2
1/2
30 
45 
3/2
2/2
5
Algebra 3 Assignment # 1
6
Trigonometric Functions
Let θ “theta” represent the measure of the reference angle.
Three basic functions are sine, cosine and tangent.
They are written as sin θ, cos θ, and tan θ
SOHCAHTOA
Right triangle trigonometry -
sin  
opp
hyp
cos  
adj
hyp
tan  
opp
adj
hyp
opp
θ
adj
A. Find cos θ
B. Find sin θ
5 2
12
θ
θ
5
13
5 3
5
C. Find tan θ
D. Find sin θ
25
9
6
θ
θ
7
7
Triangles in the Unit Circle
B (0,1)
On the Unit Circle:
P(x,y)
I
sinθ 
1
y
cosθ 
O
x
A (1,0)
tanθ 
Where functions are positive
O
II Reference Triangles
A. Drop  from point to x-axis.
8
B. Examples
3
1. Find sin   
4


coterminal angles
2. Find cos    
4
Same as cos   R 
4
3

5



coterminal angles
3. Find sin 420
=
coterminal angles
13
4. Find cos    

6
5. Find sin  =

=
cos  =
9
III Quadrangle Angles
Def: An angle that has its terminal side on one of the coordinate axes.
To find these angles , use the chart
B (0,1)
y
y
1
x
cosθ   x
1
y
sin
tanθ  
x cos
sinθ 
C (-1,0)
A (1,0)
D (0,-1)
Find the sine, cosine for all the quadrangles.
0  0 R
90 
R
2
sin 0 
cos 0 
sin 
cos 
180   R
sin

cos 
3
270   R
2
sin

cos 
360  2 R
sin

cos 
Trig values
10
Algebra 3 Assignment # 2
Complete each of the following tables please.
Radian
Measure
11
3
Degree
Measure
5
4
330
19 
6
3
45
450
210
Sin
Cos
Radian
Measure
Degree
Measure
Sin
Cos

3
2

180
7
3

4
150
11
4
780
90
11
Answers
Radian
Measure
11
3
11
6
5
4
5
2
19 
6


4
3
Degree
Measure
660
330
225
450
570
45
540
210
1

0
1
2
Sin

Cos
3
2
1
2

1
2
3
2
3
2

Degree
Measure
270
180
Sin
1
0
Cos
0
1
Radian
Measure

2
2
2

2

0

1
2
3
2

2
2
2
2
1


7
6
3
2
7
3
5
6

4
13
3
11
4

2
420
150
45
780
495
90
3
2
1
2
1
2
2
2
2
2
3
2
1
2
2
2
2

2



3
2
1
0
12
6.2 Other Trigonometric Functions
Sin
Cosecant:
Cos
Secant:
Tan
Cotangent:
http://mathplotter.lawrenceville.org/mathplotter/mathPage/trig.htm
Find the following values
1. csc
5. tan

4
4
3
2. cot

6
 
6. cot  
 4 
3. sec2
4. sec
3
2
7. csc 3
8. tan
17
6
13
6.2 Algebra 3 Assignment # 3
Complete the following tables.
8
3
Radian
Measure
Degree
Measure

6
3
4
330
5
135
450
240
Sin
Cos
Tan
Cot
Sec
Csc
Radian
Measure
Degree
Measure
Sin
Cos
Tan
Cot
Sec
Csc

3
2

540
7
3
13
4
150
7
4
210
270
Alg 3(11)
Ch 6 Trig
14
Answers
8
3
11
6
3
4
5
2

6
480
330
135
450
30
3
2
1

2

1
2
3
2
2
2
2

2
Tan
 3

1
3
1
Undef.
1
3
1
0
3
Cot

 3
1
0
3
1
Undef.
1
3
 2
Undef.
2
3
 2
1
2
2
1
2
 2
Undef.
7
3
5
6
13
4
420
150
585
210
3
2
1
2
1
2
2
2
2

2
1
2
Radian
Measure
Degree
Measure
Sin
Cos
1
3
Sec
2
2
3
Csc
2
3
2
3
2
3
Radian
Measure
Degree
Measure

270
540
Sin
1
0
Cos
0
1
Tan
Undef.
0
Cot
0
Undef.
Sec
Undef.
1
Csc
1
Undef.


 3

1
3
2

2
3
1
2
3
2
1
0

3
2

1
3
 3

2
3
2

5
4
3
900
240
3
4
135
2
2
2

2



0
1
7
6
3
2
1

2


2
3
7
4
3
2
315
270
2
2
2
2
1


3
2
1

1
3
1
Undef.
1
 3
1
0
2
3
2
Undef.
 2
 2

2
 2
0
1
Alg 3(11)
Ch 6 Trig
15
6.2 MORE TRIG FUNCTIONS
Identifying in which quadrant the angle lies is
essential for having the correct signs of the
trig functions.
If given, Sin θ =

3
and if told that 0    , can we find the cos θ?
2
5
1
θ
θ
θ
x
1. Find cos if sin = 2/3 and 0   

2
2. Find tan if sin = 3/7 and

2
 
Alg 3(11)
Ch 6 Trig
16
3. Find csc if cos =
5. If Tan  = -
3
 3
and    
2
2
4. Find sec if sin = -1/3 and
3
   2
2
4
, 270  θ<360 , find all the remaining functions of .
5
6. Find the values of the six trig. functions of , if  is an angle in standard position with the
point (-5, -12) on its terminal ray.
Alg 3(11)
Ch 6 Trig
17
Algebra 3 Assignment # 4
(1) Sin(  ) =
3
, 0 <  <  . Find the remaining 5 trig. functions of  .
2
5
(2) Cos(  ) = 
4 
,
<  <  . Find the remaining 5 trig. functions of  .
5 2
(3) Tan(  ) =
12
,  <  < 3 . Find the remaining 5 trig. functions of  .
2
5
(4) Sec(  ) =
7 3
,
<  < 2 . Find the remaining 5 trig. functions of  .
5 2
(5) Csc(  ) = 
7
, 180 <  < 270 . Find the remaining 5 trig. functions of  .
3
(6) Cot(  ) =  2 , 270 <  < 360 . Find the remaining 5 trig. functions of  .
(7) Sin(  ) = 
24
, 180 <  < 270 . Find the remaining 5 trig. functions of  .
25
(8) Find the values of the six trig. functions of , if  is an angle in standard position with the point (4 , 3) on
its terminal ray
(9) Find the values of the six trig. functions of , if  is an angle in standard position with the point (5 , 12) on
its terminal ray
Alg 3(11)
Ch 6 Trig
18
Trig Assignment #4 Answers
(1) cos(  ) = 4 , tan(  ) = 3 , cot(  ) = 4 , sec(  ) = 5 , csc(  ) = 5
5
4
3
4
3
(2) sin(  ) = 3 , tan(  ) =  3 , cot(  ) =  4 , sec(  ) =  5 , csc(  ) = 5
5
4
3
4
3
(3) sin(  ) =  12 , cos(  ) =  5 , cot(  ) = 5 , sec(  ) =  13 , csc(  ) =  13
13
13
5
12
12
(4) sin(  ) = 
5
7
2 6
2 6
, cos(  ) = 5 , tan(  ) = 
, cot(  ) = 
, csc(  ) = 
7
7
5
2 6
2 6
(5) sin(  ) =  3 , cos(  ) = 
7
(6) sin(  ) = 
1
, cos(  ) =
5
7
3
2 10
2 10
, tan(  ) =
, cot(  ) =
, sec(  ) = 
7
3
2 10
2 10
2
, tan(  ) =  1 , sec(  ) =
2
5
5
, csc(  ) =  5
2
(7) cos(  ) =  7 , tan(  ) = 24 , cot(  ) = 7 , sec(  ) =  25 , csc(  ) =  25
7
24
25
7
24
(8) sin(  ) =  3 cos(  ) = 4 , tan(  ) =  3 , cot(  ) =  4 , sec(  ) = 5 , csc(  ) =  5
5
4
3
3
5
4
(9)sin(  ) = 12 cos(  ) =  5 , tan(  ) =  12 , cot(  ) =  5 , sec(  ) =  13 , csc(  ) = 13
5
12
13
13
5
12
Alg 3(11)
Ch 6 Trig
19
Algebra 3 Review Worksheet
(1) Complete the following table please.
Rad.
Deg.
2
3
3
2
135
330
150

 9
10
3
 3
4
750
4
240
sin
cos
tan
cot
sec
csc
(2) Sin(x) = 5 ,   x   . Find the remaining 5 trig functions of x.
2
7


(3) Tan() = 1 , 0    90 . Find the remaining 5 trig functions of .
2
(4) Cot(x) = 0.8 ,   x  3 . Find the remaining 5 trig functions of x.
2


(5) Sec() = 3 , 90    180 . Find the remaining 5 trig functions of .
(6) Find the values of the six trig. functions of , if  is an angle in standard position with the
point (5 , 3) on its terminal ray.
Alg 3(11)
Ch 6 Trig
20
Algebra 3 Review Answers
(1)
2
3
3
4
3
2
11
6
 3
 5
10
3
 25
 9
4
3

Deg.
120
135
270
330
540
150
600
750
405
240
45
sin
3
2
2
2
1
1
0
1

3
2
1
 2
2

cos
1
 2
2
0
1
1
tan
 3
3
2
1

3
3
2
1
3
cot

Rad.
2
1
3
2
1
Undef
1
0
 3
Undef
Undef
2
3
1
1
2
Undef
sec
2
 2
csc
2
3
2
6
2
3

2
1
3
0

6
2
2
3
4
3
2
 2
2
2
2
1
2
2
2
1
3
1
1
1
3
1
2
2
2
3
 2
3
1
3
 3
2
3
2
2
3
2
2
3
2
 2
2

4

(2) cos(x) =  2 6 , tan(x) =  5 , cot(x) =  2 6 , sec(x) =  7 , csc(x) = 7
7
(3) sin() = 1
5
2 6
, cos() = 2 , cot() = 2 , sec() =
5
5
5
2 6
5
, csc() =
2
5
(4) sin(x) =  5 , cos(x) =  4 , tan(x) = 5 , sec(x) =  41 , csc(x) =  41
41
41
4
4
(5) sin() = 2 2 , cos() =  1 , tan() =  2 2 , cot() =  1
3
(6) sin() =
3
2 2
5
, csc() =
3
2 2
3 , cos() =  5 , tan() =  3 , cot() =  5 , sec() =  34 , csc() =
5
3
5
34
34
34
3
Alg 3(11)
Ch 6 Trig
21
ADDITION AND SUBTRACTION FORMULAS
sin
sin
cos
cos
 α +   = sin  cos  + cos  sin 
 α -   = sin  cos  - cos  sin 
 α +   = cos  cos  - sin  sin 
 α -   = cos  cos  + sin  sin 
tan  α +   =
tan   tan 
1  tan  tan 
tan  α -   =
tan   tan 
1  tan  tan 
SPECIAL ANGLES

2
30
45
60
90




6
4
3
2
2nd
3rd
4th
120
___
___
135
___
___
150
___
___
180
___
___
0 R , 2

3
2
COMBINATIONS
15  =
345  =
255  =
5
=
12
Alg 3(11)
Ch 6 Trig
22
EXAMPLES
Evaluate each expression
1) sin 75 
sin (45 + 30)
2) cos 345 
3) tan
11
12
sin(120 – 45)
Alg 3(11)
Ch 6 Trig
23
Simplify the following:
4) cos (270  - x)
5) sin ( x +

)=
2
6) cos ( x + π )
Alg 3(11)
Ch 6 Trig
24
Find each of the following numbers:
If sin A =
12

,0<A <
13
2
7) sin (A + B)
8) cos (A – B)
9) tan (A + B )
and
cos B = 
3
8
,  B 
2
17
Alg 3(11)
Ch 6 Trig
25
Algebra 3 Trig Formulas Assignment #6
(1) Find each of the following numbers please.
(a) sin(15  )
(b) cos(15  )
(c) sin(105  )
(d) cos(75  )
 13 
(e) sin 

 12 
 11 
(f) cos 

 12 
(g) sin(345  )
(h) tan(15  )
(2) Simplify each of the following please.
(a) sin(90  + x)

(b) cos(  x)
2
(c) sin(180   x)
(d) cos(  + x)
4
5
, A is in Quadrant I, Cos(B) = 
, B is in Quadrant II. Find each of the
13
5
following numbers please.
(3) Sin(A) =
(a) sin(A + B)
(b) cos(A + B)
(c) sin(A  B)
(d) cos(A  B)
(e) tan(A + B)
(f) csc(A  B)
Alg 3(11)
Ch 6 Trig
26
Assignment #6
Answers
(1)
(2)
(3)
(a)
6 
4
2
(b)
6 
4
2
(c)
6 
4
2
(d)
6 
4
2
(e)
2 
4
6
(f)
 6 
4
(g)
2 
4
6
(h) 2 
3
(a) cos x 
(b) sin x 
(c) sin x 
(d) cos x 
(a)
16
65
(b) 
(c) 
56
65
(d)
(e) 
16
63
(f) 
63
65
33
65
65
56
2
Alg 3(11)
Ch 6 Trig
27
DOUBLE AND HALF ANGLE FORMULAS
Double – Angle Formulas
Half – Angle Formulas
cos
sin 2 = 2sincos
cos 2 = cos2  - sin2 
 1 - 2sin2 

1  cos 
sin  
2
2
= 2cos 1
2
S
A
T
C
Find each of the following numbers, please.
1) sin ( 22
2) cos (
1
)
2
7
)
8

1  cos 

2
2
Alg 3(11)
Ch 6 Trig
28
If Sin A = 
5
,
13
A
3
2
Find the following numbers, please.
1
2
3) sin ( A)
4) cos (2B)
5) sin (A + B)
3
4
Tan B =  ,

B 
2
Alg 3(11)
Ch 6 Trig
29
Algebra 3 Double and Half Angle Formulas Assignment #7
(1) Find each of the following numbers please.
(a) sin(67 12  )

(b) cos  
8
 5 
(c) sin  
 8 
(d) cos(202 12  )
(2) Sin(A) =
please.
4 
12 3
, < A <  , Tan(B) = 
,
< B < 2 . Find each of the following numbers
2
5
5 2
(a) sin( 12 A)
(b) cos( 12 A)
(c) sin( 12 B)
(d) sec( 12 B)
(e) sin(2B)
(f) cos(2A)
(g) csc(A  B)
(h) cos(A + B)
Alg 3(11)
Ch 6 Trig
30
Answers
(1)
(2)
(a)
2 
2
2
(b)
2 
2
(c)
2 
2
2
(d) 
(a)
2
5
(b)
(c)
2
13
(d) 
2 
2
1
5
13
3
(e)  120
(f)  7
65
 16
(h) 33
169
(g)
25
65
2
2
Alg 3(11)
Ch 6 Trig
31
Algebra 3 Formula Review Worksheet, Assignment #8
(1) Find each of the following numbers please.
(a) sin(15  )
(b) cos(105  )
(c) sin(195  )
(d) cos(285  )
(e) sin(112 1  )
 7 
(f) cos  
 8 
(g) tan(75)
 5 
(h) sec  
 12 
2
(2) Simplify each of the following please.
(a) sin(180  + x)
(c) sin(
3
 x)
2
(3) Sin(A) = 

(b) cos( + x)
2
(d) cos(180   x)
4
13
,  < A < 3 , Sec(B) =
, 0 < B <  . Find each of the following numbers.
2
2
5
5
(a) sin(A + B)
(b) cos(A + B)
(c) sin(A  B)
(d) cos(A  B)
(e) sin(2B)
(f) cos(2A)
A
(g) sin  
2
A
(h) cos  
2
Alg 3(11)
Ch 6 Trig
32
Answers
(1)
(a)
6 
4
2
or
(c)
2 
4
6
or 
(e)
2 
2
2
(g) 2 
(2)
(3)
3
2 
2
2 
2
3
3
(b)
2 
4
6
or 
(d)
6 
4
2
or
(f) 
2 
2
2
(h)
6 
2
(a) sin x 
(b) sin x 
(c) cos x 
(d) cos x 
(a)  56
(b) 33
(c) 16
(d)  63
(e) 120
(f)  7
65
65
169
(g)
2
5
65
65
25
(h) 
1
5
2 
2
2 
2
3
3