Download Graphing

Name:
Date:
Summer Calculus BC Homework
Part 3A
Trigonometry
Period:
Seat:
Graphing
1. Identify the following functions as odd, even, or neither. Support your answer with work.
A. f ( x)  x2 sec3 x
B. f ( x)  2sec x tan x
2. For the graph below, identify the graph’s amplitude and period. Assume the graph is of a sine
wave.
Amplitude:
Period:
3. If y   34 sin(2x  56 ) , identify the graph’s amplitude and period. Do not graph.
Amplitude:
Period:
4. In the space below, graph y  2cos( 2 x  4 ) . Identify the graph’s amplitude, period, x
intercepts along one period (its primary period), and the graph’s minimum value on the
interval
1
2
 x  92 .
Amplitude:
Period:
x
x intercepts:
Min on
1
2
 x  92 :
5. In the space below, give a sketch of y  e x cos x on the interval [ 0,  ). Zoom in close
enough to provide a good idea of the nature of the graph as x increases.
x
 How many x intercepts does the graph have on [ 0,  ) ?
 What is lim e x cos x ?
x 
 Explain in your own words, why e  x cos x  e  x for all x in [ 0,  ).
Unit Circle, Best Friend (sin2x + cos2x = 1 is your “best friend” in trig), and Circle Stuff
6. The positive x – axis is rotated around the unit circle in the counter clockwise direction 1 53
times. In that case, the point (1, 0) is translated to the point P(x, y). Find the coordinates of the
point P in terms of trigonometric functions of a radian angle.
7. If csct  54 and t is in the second Quadrant, find the values of the other five trigonometric
functions of t.
8. Write cost in terms of csct if t is in the first Quadrant.
Name:
Date:
Period:
Summer Calculus BC Homework
Part 3B
Trigonometry
Seat:
Circles and Triangles
9. Give the indicated lengths in the figure below as trigonometric functions of  . Circle A is a
unit circle.
E
(1) AB
(2) BD
D
(3) BC
A
(4) CE

B
C
(5) AE
(6) DE

10. Find the value of all six trigonometric
functions given that sin  13 and
tan   0 .
12. The arc length of a sector is
11. A circle of radius 8 has a sector with
area 4 . What is the perimeter of the
sector?
13. Give the sine, cosine, and tangent of
angle A in the diagram below.
6
. The area
of the same sector is 4 . Find the
sector’s angle and radius.
7
3
A
Laws of Triangle Trigonometry
Show complete set ups and work for each of the following:
14. Using only the tangent function, express the value of x in the diagram below exactly (no
decimals!).
x
51
32
15
15. Find the remaining parts of the triangle below. Check for multiple (ambiguous) solutions.
Provide complete setups and final answers to three decimal places of accuracy
18
12
35
16. Find all of the angles in the triangle below. Provide complete setups and final answers to
three decimal places of accuracy.
16
12
24
Name:
Date:
Summer Calculus Homework
Part 3C
Trigonometry
Period:
Seat:
Formulas and Laws
17. If cos(50)  a , express tan(130) in terms of a.
18. If sin A  
2 5
8
, tan A  0, cos B   , and sin B  0 , find exact (non-calculator) values for:
5
17
A. sin( A  B) .
B. cos( A  B) .
19. Express cos(13)cos(50)  sin(13)sin(50) as a function of a single positive measure angle.
Trig Proofs and Equations
20. Prove:
sin z
 csc z  cot z
1  cos z
21. Prove:
sin 3   cos3  sec  sin 

1  2cos 2 
tan   1
Solve each of the following:
22. Solve: cos2 x  3sin x  1  0
23. Solve on 0, 2  : 3tan 2 x  tan x  0
Give decimal values for answers that are not
simple angles on the unit circle.
Substitution Stuff and Inverse Trigonometry
In each expression, make the given substitution and simplify the result.
24. In the expression
1
4
x 2  25 , make
25. In the expression
x
7  x2
substitution x  7 sin  .
the substitution x  10 tan  .
, make the
26. Express the following without using a calculator:
A. sin(cos 1 12 )
B. sin 1 (sin 54 )
C. sin(sin 1 2 )
D. cos 1 (cos 76 )
27. Express the following without using a calculator:
A. cos(tan 1 17 )
B. sin(2cos 1 53 )
C. sin(tan 1 13  cos1 14 )
D. Write as an algebraic expression
in x: sin(tan1 4x) .