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Algebra II/Trig Regents Review #10: Trig Part II
Converting degrees to radians: multiply by

180
Example:
1.
2. 135
75
Converting radians to degree: multiply by
1.

180
2.
4
or replace pi with 180

5
12
3. 4 radians
Example Regents Questions
1.
What is the number of degrees in an angle whose radian measure is
(1) 150
2.
(2) 165
11
?
12
(3) 330
(4) 518

o
What is the radian measure of an angle whose measure is 420 ?
(1) 
7
3
(2) 
7
6

(3)
7
6
(4)
7
3
3. What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock?

(1)

2

(2)
5
6

(3)
2
3

(4)
4. Find, to the nearest tenth of a degree, the angle whose measure is 2.5 radians.




7
6
Find the Length of the intercepted arc: We use the formula:
s r
s = intercepted arc
 = central angle(in radians)
r = radius
1.
Find the measure of the central angle of a circle with a radius of 2.5 meters and an intercepted arc of 10 meters.
2.
If the length of the radius of a circle is 8 meters and the central angle is 30 degrees, finr the length of the
intercepted arc.
1.
Example Regents Questions
A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2
radians?
(1) 2

2.
(3) 8
(2) 2
(4) 8

In circle O, the length of the radius is 8 cm. If the central angle measures 45 o, what is the length of the
intercepted arc?

Finding the exact value of trig functions with angles in radians: Convert to degrees and use QSRV
Example: sin

6

1. Write tan 140
2. Write cot
tan
5
3
Example Regents Questions
 as a function of a positive acute angle.
17
as a function of a positive acute angle (in radians).
18

3.
sec

4. tan 4  sin 

5.



5
6
 5 2
cot 

6 
23 

6 
Finding trig values of an unknown angle: **Label each function with the correct sign first** The triangle always starts at
the origin**
1.
If sin   
4
and theta is in Quadrant II. Find the remaining five trig functions.
5
2.
If cot   
4
and theta is in Quadrant IV, find all other trig functions.
3
Example Regents Questions
1.
If sin  


2.

3
and tan  < 0 , what is the value of cos ?
5
If cos  

8
and  is in Quadrant I, what is the value of (csc  )(tan  ) ?
10

Inverse Functions: switching the function value and the angle
y  arccos x
y  arcsin x
y  arctan x
1
y  cos x
1
y  sin x
y  tan 1 x
Examples:
3
2
arcsin
1.

2. arccos 
 1 
 2 

3. cos  sin 1    

2
2
 3 
 5 
4. tan  sin 1   

Example Regents Questions

1.
3 
?
 2 
What is the principal value of cos1
o
(1) 30
o
(2) 60
(3) 150
o
o
(4) 240


2.

 3.
5 
8 


If sin 1  A, then
(1) sin A 
5
8
(2) sin A 
8
5
 3 
]
 2 
Find the value oftan[cos 1


(3) cos A 

5
8
(4) cos A 

8
5
Cofunctions:
sin   cos  90   
cos   sin  90   
tan   cot  90   
cot   tan  90   
or
sec   csc  90   
csc   sec  90   
Examples:
1. Find the value of theta for which sin   cos15 .
2. Write the expression tan 265 as the function of an acute angle of measure less than 45 .
3. If x is the measure of a positive acute angle, solve for x. sin  x  15   cos  2 x 
Example Regents Questions
1.

 2.
2
If A is acute and tan A  , then
3
2

(1) cot A
3
(2) cot A 
1
3
(3) cot(90 o  A) 
o

What is the trigonometric
function that isequivalent to sec 35 ?

2
3
(4) cot(90 o  A) 

1
3