Unit 5 Pre calc test 1

Question 1

converting radians to degrees

Answer 1

radians = degrees times (pi/i80)
ex. 60degrees times pi/180 = pi/3
do 60/180 to get the 3

Question 2

converting degrees to radians

Answer 2

degrees = radians times (180/pi)
ex. 5pi/18 times 180/pi = 50 degrees
do 5/18 times 180 to get 50

Question 3

how would you find the coterminal angle of 300 degrees?

Answer 3

to find the positive you would 360 for negative subtract 360

Question 4

how would you find the coterminal angle of 5pi/6

Answer 4

to find the positive you would add a version of 2pi so the denominators match (for this ex it would be 12pi/6) to find the negative you would subtract that same version of 2pi

Question 5

A circle has a radius of 8cm and a central angle of 5pi/6
a. measure of the intercepted arc?
b. area of the sector?

Answer 5

a. use the equation s=theta times r to find the answer (theta is the central angle)
b. use the equation 1/2 times theta times r^2

Question 6

what do sin cos and tan correspond to?

Answer 6

csc sec and cot

Question 7

what are each of the following in terms of sin and cos
a. tan(theta)
b. sec(theta)
c. csc(theta)
d. cot(theta)

Answer 7

a. sin/cos
b. 1/cos
c. 1/sin
d. cos/sin

Question 8

what is the linear speed formula?

Answer 8

use 2pi(r) to convert the rev then just do more unit conversions

Question 9

what is the angular speed formula

Answer 9

w= theta/t

Question 10

what is this angle in degree minute second (DMS) form?
36.875degrees

Answer 10

36 is the thing that remains degrees
you then take the 0.875 and multiply it by 60(or60/1) which gives you 52.5
you then take the 0.5 and multiply it by 60(or60/1) which gives you 30
this all together gives the answer of 36 degrees 52^I 30 ^II

Question 11

What is this angle measure in decimal degree form?
-98degrees 12^I 48^II

Answer 11

-98 is the thing that remains as degrees
you then take the 12 and multiply it by 1/60 which gives you 0.2
then you take the 48 and multiply it by 1/3600 which gives you 0.0133333
all together this gives you the answer of -98.213

Question 12

what are inverse sin cos and tan

Answer 12

theta = sin^-1(x)
theta = cos^-1(x)
theta = tan^-1(x)

Question 13

a. what are the side lengths of a 30-60-90 triangle in relation to the 30
b. what are the side lengths of a 45-45-90 triangle in relation to the 45

Answer 13

a. opposite: 1
adjacent: square root of 3
Hyp: 2
b. opposite: 1
adjacent: 1
Hyp: square root of 2