a' sin 135

1
AP Calculus Summer 2009 Assignment 2 Topic
Working with Trigonometry Name___________________
_
1) i. Find the exact value of without using a
calculator
a. sin (135?)
b. cos( 240? )
c. tan ( )
c. sec ( )
ii. Explain how to evaluate these ratios without
a calculator.
2) Find the values of all six trigonometric
functions for the angle ? of the right
triangle with legs of length 1 and 4 as shown to
the right.
c
1
?
4
3) Two students are 180 feet apart on opposite
sides of a telephone pole. The angles
of elevation from the students to the top of the
pole are 35? and 23? . a. Draw a diagram
for this situation.
b. Find the height of the telephone pole.
2
4) Analytically find all possible solutions
for x in the interval ( 0, 2? ). Leave
answers exact. a. b.
5) Given f(x) ? 3 cos ( 2x ? ? ) ? 1

• b. Sketch one cycle of f(x).
• Remember to label your axes

• a. Describe how to determine amplitude,
  period,
• and phase shift from this equation.

6) Find the exact value of each composition
without using a calculator.
p
a. sin ( tan-1 ( -1 ) )
v
b. arcsin ( cos ( ) )
c. tan ( sec-1 )
2
6
7) Write each expression in terms of sine and
cosine, and then simplify.
tan x
a.
b. sin x cot x cos x
sec x
8) Verify that the following equations is an
identity 1 sec x sin x tan x sec2x
3
AP Calculus Summer 2009 Assignment 2 Topic
Working with Rational Equations Name_____________
_______
. Find
Let
, the inverse of
9)
11). Simplify the expressions with rational
exponents.
b. ( ) -3
a3/2 b2/3
a2
12) Simplify each expression.
4

• 13) a. Sketch each graph correctly. Indicate all
  asymptotes and wholes.
• Hint the graphic calculators graph is NOT
  correct.
• b. For each function explain verify the
  domain analytically (without the graph)

http//coolmath.com/algebra/PreCalc/index.htmlGra
phing_Rational_Functions