Trigonometric Identities
Double Angle Identities
Basic Identities
1
csc x
1
cos x =
sec x
1
tan x =
cot x
sin( x) = sin x
sin x =
sin x
cos x
cos x
cot x =
sin x
tan x =
sin 2 x = 2 sin x cos x
cos 2 x = cos 2 x sin 2 x
= 1 2 sin 2 x
= 2 cos 2 x 1
tan 2 x
Chapter 3 Review
1) Use the definition of the derivative to find the derivative of f ( x) x 2 2 x at x = 5. Show your work.
2) Sketch a possible graph of a continuous function f that has domain [-3, 3], where f (-1) = -1 and the graph of
y = f (x) is show
Chapter 10 Review
1) Let u 2, 4 and v 3, 5 .
a) Find 2u v
b) Find the magnitude of 2u v
c) Find u v .
2) An airplane, flying in the direction 50 east of north at 375 mph in still air, encounters a 45 mph wind
blowing from the north (i.e., the wind directi
Chapter 7 Review
1) What is the area of the shaded region shown?
2) What is the area enclosed by x y , x 6 y and
the x-axis? (Use a horizontal rectangle.)
3) Find the area enclosed by y 3 x , y 20 2 x , and
the x-axis.
A) 39.5736
B) 45.3125
C) 46.7382
D)
Chapter 6 Review
1) Evaluate the indefinite integral
x
23
9 5 x 3 dx ,
2) Which of the following is the result when the Fundamental Theorem of Calculus is used to evaluate
sin(e x 4 x)dx ?
x
A)
sin(e
0
t
4t )dt C
B)
0
sin(e
t
4t )dt C
C) (e x 4) cos(e
Chapter 9 Review
1) Write the first four terms of the series
x2n
n 3 ( n 2)!
n
3
2) Tell whether the series 5 converges or diverges. If it converges, find its sum.
n 1 4
3) Express the repeating decimal 0.73 as a geometric series and find its sum.
x 2 x3
Chapter 2 Review
1) Use the graph to estimate the limits and value of the function, or explain why the limits do not exist.
A) lim f ( x)
B) lim f ( x)
2) Determine the limit by substitution.
D) f (2)
C) lim f ( x)
x2
x2
x 2
lim (6 x 2 5 x 12)
x 2
3) Assu
Chapter 4 Review
1) Use the graph of y = f(x) to estimate the answer to the following questions.
a)
b)
c)
d)
e)
Find the local extreme values and where they occur.
For what values of x is f '( x) 0 ?
For what values of x is f '( x) 0 ?
For what values of
Chapter 8 Review
1) Write a recursive formula for the sequence cfw_1, -1, 3, -5, 11,
2) What is the first term of an arithmetic sequence with 101st term 32 and common difference 0.3?
3) What is the common ratio of a geometric sequence with 8th term 13122
Chapter 5 Review
1) Consider the region enclosed between the graph of f ( x) e x x3 and the x-axis for 1 x 3.5 .
a) Find MRAM5, the area estimate obtained using 5 midpoint rectangles.
b) Use MRAM to estimate the area with accuracy of 2 decimal places.
3
4
Week One Quiz
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1. Shareholder wealth is measured by the _B_.
2. The net present value rule provides appropriate guidance for financial