Expert: Sherman D. - 11/4/2008

Question
QUESTION: Sherman, Can you please check these for me? I'd really appreciate it. Thanks.


1) Convert 18 degrees to radians.
      I think it is C

Has to be either...

a) 3.14 / 10
b) -3.14
c) 0
d) 3.14



2) Convert -4 PIE to degrees
      I think it is D

Has to be either...

a) 1440 degrees
b) -1440 degrees
c) -720 degrees
d) 720 degrees


3) Which angle below is co-terminal to 415 degrees?
         I think it is A

Has to be either...

a) 85 degrees
b) -85 degrees
c) -55 degrees
d) 55 degrees


4) Find the length of the arc on a circle of radius r = 16 inches by a central angle 0 = 60 degrees
   I think it is B

Has to be either...

a) 20 inches
b) 1.5 inches
c) 16.76 inches
d) 100 inches


5) Given sin 0 = 3/5 and cos0 = 4/5, find tan 0
         I think its D

Has to be either...

a) 4/5
b) 1/4
c) 3/4
d) 1


6) Given sin 0 = 3/5 and cos0 = 4/5, find sec0
         I think its C

Has to be either...

a) 4/5
b) 3/4
c) 1
d) 5/4


7) Simplify sin^2 + cos^2  3.14/10
         I think its A

Has to be either...

a) 2
b) 1
c) 3
d) 10


8) Which of the following expressions represents the same value as sin 19 degrees?
      I think its D

Has to be either...

a) Cos 19 degrees
b) Tan 19 degrees
c) Cos 71 degrees
d) Csc 71 degrees


9) Which of the following expressions represents the same value as csc 35 degrees?

  I think its A

Has to be either...

a) Sec 55 degrees
b) Cos 55 degrees
c) Tan 55 degrees
d) Cot 55 degrees


10) Given sin 0 = 2/3 and cos 0 = square root of 5 over 3, find cot 0
         I think its C

Has to be either...

a) square root of 5 over 2
b) square root of 5 over 4
c) 1
d) 1/4



11) Given sin 0 = 2/3 and cos 0 = square root of 5/ 3, find csc 0
         I think its B

Has to be either...

a) 1
b) square root of 5 over 2
c) 2/3
d) 3/2





12) Given a point (-5, 5) on the terminal side of the angle 0, find value of sin 0
       A

Has to be either...

a) 1/2
b) -1/2
c) - square root of 2 over 2
d) square root of 2 over 2


13) Give a point (5, -5) on the terminal side of angle 0, find the value of tan 0
       C

Has to be either...

a) square root of 2
b) -1
c) 1
d) negative square root of 2


14) Give a point (5, -5) on the terminal side of angle 0, find the value of sec 0
     D

Has to be either...

a) square root of 2
b) -1
c) 1
d) negative square root of 2


15) Evaluate the quadrantal angle csc pie (3.14)
         B

Has to be either...

a) -1
b) 1
c) 0
d) Undefined


16) Let 0 be an angle in the standard position. Name the quadrant in which 0 lies, if sin 0 <0, cos 0>0
         A

Has to be either...

a) I
b) II
c) III
d) IV



17) Find the reference angle for 170 degrees
       D

Has to be either...

a) 100 degrees
b) 20 degrees
c) 10 degrees
d) 30 degrees


18) Find the reference angle for -17PIE / 6
     C

Has to be either...

a) 3.14/6
b) -3.14/6
c) -3.14
d) 3.14



19) Find the value of sin 300 degrees
      B

Has to be either...

a) square root of 2 over 2
b) negative square root of 3 over 2
c) square root of 3
d) square root of 2


20) Find the value of tan 3PIE /2
         D

Has to be either...

a) -1
b) 1
c) Undefined
d) 0


21) Using unit circle properties, find the value of cos 3.14/3
         B

Has to  be either...

a) 1
b) 1/2
c) - 1/2
d) 0


22) Using the circle properties, find the value of tan {-11PIE /6}
         D

Has to be either...

a) square root of 3 over 3
b) square root of 3 over 2
c) square root of 3
d) 1/2



23) Find the value of tan 0
        A

Has to be either...

a) Undefined
b) 1
c) 0
d) -1



24) Use periodic function to find the value of cos 11PIE / 4  
        C

Has to be either...

a) square root of 2
b) -1/2
c) - square root of 2 over 2
d) square root of 2 over 2


25) Use periodic function to find the value of cot 15PIE / 2
         B

Has to be either...

a) square root of 2
b) 0
c) 1
d) Undefined




ANSWER: 1) Convert 18 degrees to radians.
     I think it is C

Has to be either...

a) 3.14 / 10
b) -3.14
c) 0
d) 3.14

18pi/180 = pi/10 or 3.14/10

ANS : A.

----------------------------------------

2) Convert -4 PIE to degrees
     I think it is D

Has to be either...

a) 1440 degrees
b) -1440 degrees
c) -720 degrees
d) 720 degrees

-4pi * 180/pi = -720

ANS : C.

--------------------------------------

3) Which angle below is co-terminal to 415 degrees?
         I think it is A

Has to be either...

a) 85 degrees
b) -85 degrees
c) -55 degrees
d) 55 degrees

415 - 360 = 55

ANS : D.

--------------------------------

4) Find the length of the arc on a circle of radius r = 16 inches by a central angle 0 = 60 degrees
  I think it is B

Has to be either...

a) 20 inches
b) 1.5 inches
c) 16.76 inches
d) 100 inches

s = 16(60pi/180)
s = 16.76
ANS : C.

----------------------------------

5) Given sin 0 = 3/5 and cos0 = 4/5, find tan 0
         I think its D

Has to be either...

a) 4/5
b) 1/4
c) 3/4
d) 1

sin(A) = 3/5
cos(A) = 4/5

tan(A) = sin(A)/cos(A)
tan(A) = (3/5)/(4/5)
tan(A) = (3/4)
ANS : C.

-------------------------------------

6) Given sin 0 = 3/5 and cos0 = 4/5, find sec0
         I think its C

Has to be either...

a) 4/5
b) 3/4
c) 1
d) 5/4

sec(A) = 1/cos(A)
cos(A) = 4/5
sec(A) = 1/(4/5) = 5/4
ANS : D.

----------------------------------------

7) Simplify sin^2 + cos^2  3.14/10
        I think its A

Has to be either...

a) 2
b) 1
c) 3
d) 10

sin(A)^2 + cos(A)^2

i don't know what you meant by the 3.14/10, but sin(A)^2 + cos(A)^2 = 1

ANS : B.


---------------------------------------

8) Which of the following expressions represents the same value as sin 19 degrees?
     I think its D

Has to be either...

a) Cos 19 degrees
b) Tan 19 degrees
c) Cos 71 degrees
d) Csc 71 degrees

ANS : ANS : C.

--------------------------------

9) Which of the following expressions represents the same value as csc 35 degrees?

 I think its A

Has to be either...

a) Sec 55 degrees
b) Cos 55 degrees
c) Tan 55 degrees
d) Cot 55 degrees

ANS : A.

------------------------------------

10) Given sin 0 = 2/3 and cos 0 = square root of 5 over 3, find cot 0
        I think its C

Has to be either...

a) square root of 5 over 2
b) square root of 5 over 4
c) 1
d) 1/4

cot(A) = cos(A)/sin(A)
cot(A) = (sqrt(5)/3)/(2/3)
cot(A) = sqrt(5)/2
ANS : A.

---------------------------------

11) Given sin 0 = 2/3 and cos 0 = square root of 5/ 3, find csc 0
         I think its B

Has to be either...

a) 1
b) square root of 5 over 2
c) 2/3
d) 3/2

csc(A) = 1/sin(A) = 1/(2/3) = 3/2
ANS : D.

---------------------------------

12) Given a point (-5, 5) on the terminal side of the angle 0, find value of sin 0
      A

Has to be either...

a) 1/2
b) -1/2
c) - square root of 2 over 2
d) square root of 2 over 2

sin(A) = y/r

(-5)^2 + (5)^2 = r^2
r = 5sqrt(2)

sin(A) = -5/5sqrt(2) = -1/sqrt(2) = -sqrt(2)/2
ANS : C.

-------------------------------------

13) Give a point (5, -5) on the terminal side of angle 0, find the value of tan 0
      C

Has to be either...

a) square root of 2
b) -1
c) 1
d) negative square root of 2

tan(A) = y/x
tan(A) = -5/5 = -1
ANS : B.)

-----------------------------------

14) Give a point (5, -5) on the terminal side of angle 0, find the value of sec 0
    D

Has to be either...

a) square root of 2
b) -1
c) 1
d) negative square root of 2

sec(A) = r/x

5^2 + (-5)^2 = r^2
25 + 25 = r^2
r^2 = 50
r = 5sqrt(2)

sec(A) = 5sqrt(2)/5 = sqrt(2)
ANS : A

-----------------------------------

15) Evaluate the quadrantal angle csc pie (3.14)
        B

Has to be either...

a) -1
b) 1
c) 0
d) Undefined

csc(pi) = 1/sin(pi) = 1/0
ANS : D.

-----------------------------------

16) Let 0 be an angle in the standard position. Name the quadrant in which 0 lies, if sin 0 <0, cos 0>0
         A

Has to be either...

a) I
b) II
c) III
d) IV

sin(A) < 0, cos(A) > 0
sin(A) < 0, when A = III and IV
cos(A) > 0, when A = I and IV
ANS : D.

-------------------------------------

17) Find the reference angle for 170 degrees
      D

Has to be either...

a) 100 degrees
b) 20 degrees
c) 10 degrees
d) 30 degrees

ANS : C.

--------------------------------------

18) Find the reference angle for -17PIE / 6
    C

Has to be either...

a) 3.14/6
b) -3.14/6
c) -3.14
d) 3.14

-17pi/6 = -512 = -150 = 210
the reference angle of 210 is 30, which is like saying pi/6

ANS : A.

--------------------------------------

19) Find the value of sin 300 degrees
     B

Has to be either...

a) square root of 2 over 2
b) negative square root of 3 over 2
c) square root of 3
d) square root of 2

sin(300) = -sqrt(3)/2
ANS : B.

-----------------------------------

20) Find the value of tan 3PIE /2
         D

Has to be either...

a) -1
b) 1
c) Undefined
d) 0

tan(3pi/2) = sin(3pi/2)/cos(3pi/2) = -1/0 = undefined
ANS : C.

-------------------------------------

21) Using unit circle properties, find the value of cos 3.14/3
         B

Has to  be either...

a) 1
b) 1/2
c) - 1/2
d) 0

cos(pi/3) = (1/2)
ANS : B.

Remember pi is also like saying 180, so pi/3 = 180/3 = 60

-----------------------------------

22) Using the circle properties, find the value of tan {-11PIE /6}
         D

Has to be either...

a) square root of 3 over 3
b) square root of 3 over 2
c) square root of 3
d) 1/2

tan(-11pi/6) = sqrt(3)/3
ANS = A.

-------------------------------------------

23) Find the value of tan 0
       A

Has to be either...

a) Undefined
b) 1
c) 0
d) -1

tan(0) = sin(0)/cos(0) = 0/1 = 0
ANS : C.

------------------------------------------

24) Use periodic function to find the value of cos 11PIE / 4  
       C

Has to be either...

a) square root of 2
b) -1/2
c) - square root of 2 over 2
d) square root of 2 over 2

cos(11pi/4) = -sqrt(2)/2
ANS : C.)

--------------------------------------------------

25) Use periodic function to find the value of cot 15PIE / 2
         B

Has to be either...

a) square root of 2
b) 0
c) 1
d) Undefined

cot(15pi/2) = cos(15pi/2)/sin(15pi/2) = 0/-1 = 0
ANS : B.)

www.krellinst.org/uces/archive/resources/trig/node10.html

www.analyzemath.com/Angle/reference_angle.html

http://id.mind.net/~zona/mmts/trigonometryRealms/TrigFuncPointDef/TrigFuncPointD

your computer has a scientific calculator, so all you have to do is work it on that.

unless your a mom/father trying to help their child, but if your not, i want to see some "the answer is" and less "i think its"

especially when your "i think its" aren't even close to the correct answer.

---------- FOLLOW-UP ----------

QUESTION: Thanks for all of your help. I really do appreciate it. I have a couple more questions...

1) Is 177 degrees an Obtuse angle?

2) When evaluating csc45 degrees in a 90 degree angle, would I get the square root of 3?

It has to be either, the square root of 3, square root of 2, -1, or 1.

Answer
1.) that question is so easy here is what i'm going to do, i'm going to teach you how to google something.

go to www.google.com and search for Obtuse Angels, some will also say just google obtuse angles.

------------------------

2.)
csc(45) = 1/sin(45)

sin(45) = sin(90/2)

sin(90/2) = sqrt((1 - cos(90))/2) = sqrt((1 - 0)/2) = sqrt(1/2) = sqrt(2)/2

so

csc(45) = 1/(sqrt(2)/2) = 2/sqrt(2) = 2sqrt(2)/2 = sqrt(2)