Transcript Slide 1

Students,
Take out your calendar and your homework. Take out your spiral
notebook and Complete the DNA. Use your notes if
necessary.
Convert the following
angle to radians or vice
versa.
1) 225
2
2)
3
3)  1.57
Use your calculator to
evaluate the following:
4) cos67
 6 
5) tan 
 7 
 
6) csc  
 7
Trigonometric Values
of Common Angles
 1 3
 2, 2 



(–1, 0)

3 1
 2 , 2 



2
 2 ,

90°
2
3 3 120°
5 4 135°
6 150°

2 2
 2 , 2 



3,1

 2 2


y (0, 1)
180°

2

1 3
2, 2 


60° 3
45°

 2 2
 2 , 2 


4 
30° 6
x
0° 0
360° 2 (1, 0)
330°
11
315°
 3 1
7 210°
6
6
225°
7
5
240° 300°
2  4 4
5 4 


2 
3


3
3 270° 2
 1
3

,

 2
2 

 3 1
 2 ,2


(0, –1)
1
3
,

2
2 

 2 , 2 


2 , 2 
2
2 
Find the indicated trig ratio below.
2
3
1) sin

3
2
2 2 3
5) csc

3
3
5
3
2) cos  
6
2
5
2
3
6) sec

6
3
11
3
3) t an

6
3
1
4) cos(60) 
2
11
7) cot
 3
6
1
8) cos(60) 
2
Use a calculator to find the trig ratios.
1) t an 48
2) t an(5.22)
 2 
3) cos

 7 
4) t an 35
 4 
5) csc

 11 
6) sec(11)
  2 
7) cot

 7 
EVEN and ODD Trig functions
The cosine and secant functions are even.
cos t   cost
sec t   sec t
The sine, tangent, cosecant, and cotangent
functions are odd.
sin  t    sin t
csc t    csc t
tan t    tant
cot t    cot t
Sine and cosine are periodic functions.
sint  2n  sin t
cost  2n  cost
f t   sin t
f t   cost
dom ai n:  ,  
dom ai n:  ,  
ran ge: [1,1]
ran ge: [1,1]
2
1) Evaluate the six trig functions of t  
.
3
2) Evaluate the following without a calculator.
9
a) cos
3
 11 
b) sin  

 2 
2
3) If tan t   , find tan  t .
3
4) Use a calculator to evaluate.
5
a) sin
7
b) csc 2
Arc Le n gth
s  r
1) A circle has a radius of
27 inches. Find the
length of the arc
intercepted by a central
angle of 160°.
Linear and Angular Speed
arc length s
Linear speed 

time
t
central angle 
angular speed 

time
t
2) The circular blade on a saw rotates at 2400
revolutions per minute.
a)Find the angular speed in radians per second.
b)The blade has a radius of 4 inches. Find the linear
speed of a blade tip in inches per second.
1) C on ve rt60 from de gre e sto radian s.
2) Fin d th esu pple m e nof
t an an gle
5
m e asu ring 
.
7
3) O na circlewitha radiu sof 9
in ch e s,fin dth e le n gthof th earc
in te rce pte
d by a ce n tralan gleof 140.