Pre-Calculus. Chapter 4A Review - Solutions. The Chapter 4A Test will cover Sections 4.1, 4.2, and 4.4. It will also include ... 11) The point ( ) is ...
Name ___________________________________ Date __________________________ Period _______ Pre-Calculus
Chapter 4A Review - Solutions The Chapter 4A Test will cover Sections 4.1, 4.2, and 4.4. It will also include cofunctions from section 4.3. Things you should be able to do:
Find the exact value of any trigonometric function of any angle on the unit circle.
Answer the following questions without the use of a calculator. You may not use a calculator on the Chapter 4A Test. You may use a unit circle on these problems; you will be given a blank copy for your test. 1) In what quadrant is ? Quadrant I. is coterminal with 2) Find the complement and supplement (if they exist) of Since is greater than , there is no complement. The supplement is
.
3) Find the complement and supplement (if they exist) of Complement: Supplement: 4) Find a positive angle less than 5) Find a positive angle less than
6) Convert
that is coterminal with that is coterminal with
to radians. (
7) Convert
)
to degrees. (
)
(
)
. .
Name ___________________________________ Date __________________________ Period _______ Pre-Calculus √
8) The point (
) is on the unit circle, and is on the terminal side of . Find the value of all six
trigonometric functions of . Since the point is on the unit circle, ( ) √
( )
√
( )
√
√
( ) √
( )
√ √
( ) 9) Given
√
and ( ) ( ) ( )
√ √
, find the value of the other four trigonometric functions. ( ) ( )
√ √
√
( ) √ ( )
√ √
√ √
( ) ( ) 10) Find a cofunction with the same value as . ( ) ( ) ) is on the terminal side of . Find the value of all six trigonometric functions of 11) The point ( . ( )
√
√
√ ( ) ( ) ( ) ( ) ( ) ( )
√
Name ___________________________________ Date __________________________ Period _______ Pre-Calculus 12) In what quadrant is if and ( ) in quadrants I and III ( ) in quadrants III and IV Both requirements are met in quadrant III 13) Given Since
and ( )
?
is in quadrant IV, find the value of the other five trigonometric functions.
we can set
and
. We then can use the Pythagorean Theorem to
find . √ Since
is in quadrant IV, √
√ √
( )
√
( ) √
( )
√
( )
√ √
( )
√
14) Find the reference angle for . Since is in quadrant II, its reference angle is 15) Find the reference angle for Since
.
is in quadrant II, its reference angle is
16) The formula states that the linear speed, , of an object is equal to the radius of the circle it is traveling, , times the rotational speed (also called angular speed) of the circle it is travelling, . What is the linear speed (in meters per second) of an object that is traveling in a circle of radius four meters, travelling at 5 revolutions per second? First, we must convert from revolutions per second to radians per second.
