Download Tutorial_1.1

PTG 0016 Trigonometry and Coordinate Geometry
Tutorial 1.1: Trigonometric Functions
1) Draw each angle.
a) 135°
b) 450°
c)
2) Convert each angle to a decimal in degrees. Round the answer to two decimal places.
a) 40° 10’ 25’’
b) 9° 9’ 9’’
3) Convert each angle to DMS form. Round the answer to the nearest seconds.
a) 40.32°
b) 18.255°
4) Convert each angle in degrees to radians. Express the answer as a multiple of .
a) 30°
b) 180°
c) -135°
5) Convert each angle in radians to degrees.
a)
b)
6) Convert each angle in degrees to radians. Express your answer in decimal form,
rounded to two decimal places.
a) -40°
b) 125°
7) Convert each angle in radians to degrees. Express your answer in decimal form,
rounded to two decimal places.
a) 3.14
b) 6.32
8) Find the values of the six trigonometric functions of the angle
(a)
in each figure.
5
12
(b)
(c)
3
1
2
9) Use identities to find the exact value of each of the four remaining trigonometric
functions of the acute angle .
a)
= ,
=
b)
= ,
=
10) Use the definition or identities to find the exact value of each of the remaining five
trigonometric functions of the acute angle .
a)
=
b)
=
c)
=2
11) Use Fundamental Identities and/or the Complementary Angle Theorem to find the
exact value of each expression. Do not use a calculator.
a)
°+
°
b)
c)
-
d)
-
e)
f) 1 -
°-
g)
-
h)
i)
.
.
+
= , use trigonometric identities to find the exact value of
12) Given
a)
b)
c)
°
°
d)
13) Given
a)
b)
c)
=
, use trigonometric identities to find the exact value of
°
d)
14) Given
a)
b)
c)
d)
=
use trigonometric identities to find the exact value of
15) Given
a)
b)
c)
d)
=
use trigonometric identities to find the exact value of
16) Given the approximation
exact value of
a)
b)
c)
d)
e)
f)
g)
h)
, use trigonometric identities to find the
17) Given f ( ) =
calculator.
. Find the exact value of each expression if
= 60 . Do not use a
a)
b) f ( )
c) [f( )] 2
d) 2 f( )
e)
18) Find the exact value of each expression. Do not use a calculator.
a)
b)
+
c)
d)
-4
°+
°
19) Use a calculator to find the approximate value of each expression. Round the answer
to two decimal places.
a)
b)
c)
d)
e)
20) A point on the terminal side of an angle
six trigonometric function of
a) (-3, 4)
b) (2, -3)
is given. Find the exact value of each of the
c) (
21) Use a coterminal angle to find the exact value of each expression. Do not use a
calculator.
a)
b)
22) Name the quadrant in which the angle
a)
b)
23) Find the reference angle of each angle.
a) -30
b) 120
c) 210
d)
e)
f) -135
g)
h)
i)
24) Use the reference angle to find the exact value of each expression. Do not use a
calculator.
a)
b)
c)
d)
e)
f)
g)
h)
25) Find the exact value of each of the remaining trigonometric functions of
,
a)
=
b)
=
c)
=
d)
e)
=
,
= 2,
,
,
26) Use the fact that the trigonometric functions are periodic to find the exact value of
each expression. Do not use a calculator.
a) sin 405
b) tan 405
c) csc 450
d) cot 390
e)
f)
g)
h)
27) Use the even-odd properties to find the exact value of each expression. Do not use a
calculator.
a) sin(-60°)
b) tan(-30°)
c)
d)
e)
28) Find the exact value of each expression. Do not use a calculator.
a)
+
b)
+
29) Determine the amplitude and period of each function without graphing.
a) y = -sin( )
b) y = 6 sin(πx)
c) y = 30) Graph each function. Be sure to label key points and show at least two cycles.
a) y = 4 cos (x)
b) y = cos(4x)
c) y = - cos(2x)
d) y = 2 sin(x) + 3
e) y = -6
+4
f) y = 5 – 3 sin(2x)