Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 3
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411. Convert the angle
12 to degrees and the angle 900 to radians. Give exact answers.
2. Suppose that sin( ) = 5 13 and cos( ) =
12 13. Find the values of tan( ), cot( ), csc( ), and sec( ).
Find the value of tan(2 ).
3. If
2
3
2 and tan = 4 3, find sin , cos , cot , sec , and csc .
4. Find all solutions of the equations a) sin( ) =
3 2, b) tan( ) = 1.
5. A ladder that is 6 meters long leans against a wall so that the bottom of the ladder is 2 meters from the
base of the wall. Make a sketch illustrating the given information and answer the following questions.
How high on the wall is the top of the ladder located? What angle does the top of the ladder form
with the wall?
6. Let
be the center of a circle whose circumference is 48 centimeters. Let
and
be two points on
the circle that are endpoints of an arc that is 6 centimeters long. Find the angle between the segments
and
. Express your answer in radians.
Find the distance between
and
.
7. The center of a clock is located at the origin so that 12 lies on the positive -axis and the 3 lies on the
positive -axis. The minute hand is 10 units long and the hour hand is 7 units. Find the coordinates
of the tips of the minute hand and hour hand at 9:50 am on Newton’s birthday.
8. Find all solutions to the following equations in the interval [0 2 ]. You will need to use some trigono-
metric identities.
2
(a)
3 cos( ) + 2 tan( ) cos
( ) = 0
(c) 2 cos( ) + sin(2 ) = 0
2
(b) 3 cot
( ) = 1
9. A function is said to be periodic with period
if ( ) = ( + ) for any . Find the smallest, positive
period of the following trigonometric functions. Assume that
is positive.
(a) sin
(b) sin(3 ).
(c) sin ( ) + cos ( ).
2
(d) tan
( ).
10. Find a quadratic function ( ) so that the graph
has -intercepts at
= 2 and
= 5 and the
-intercept is
=
2.
11. Find the exact values of the following expressions. Do not use a calculator.
1
1
(a) tan
(1)
(c) sin
(sin(7
3))
1
1
(b) tan(tan
(10))
(d) tan(sin
(0 8))
1
12. Give a simple expression for sin(cos
( )).
13. Let
be the function with domain [
2 3
2] with ( ) = sin( ) for
in [
2 3
2]. Since
is one
to one, we may let
be the inverse function of . Give the domain and range of . Find (1 2).
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