Chapter 6: Review

Question 1

180 degress =

Answer 1

pi radians

Question 2

1 radian =

Answer 2

(180/pi)

Question 3

1 degree =

Answer 3

(pi/180 radians)

Question 4

Coterminal angles

Answer 4

angles that end in the same place

Question 5

length of a circular arc

Answer 5

s=rΘ (Θ is in radians)

Question 6

area of a sector

Answer 6

A=1/2r²Θ (Θ is in radians)

Question 7

angular speed

Answer 7

w = Θ/t

Question 8

linear speed

Answer 8

v = s/t

Question 9

angle of elevation

Answer 9

looking up from horizon

Question 10

angle of depression

Answer 10

looking down from horizon

Question 11

sinΘ =

Answer 11

y/r

Question 12

cosΘ =

Answer 12

x/r

Question 13

tanΘ =

Answer 13

y/x

Question 14

cscΘ =

Answer 14

r/y

Question 15

cosΘ =

Answer 15

r/x

Question 16

cotΘ =

Answer 16

x/y

Question 17

reference angle

Answer 17

the acute angle formed by the terminal side of the angle and x-axis

Question 18

area of a triangle

Answer 18

A=1/2bh (find height with trig)

Question 19

domain and range of y=sinx

Answer 19

domain: [-pi/2, pi/2]
range: [-1, 1]

Question 20

domain and range of y=cosx

Answer 20

domain: [0,pi]
range: [-1, 1]

Question 21

y=tanx

Answer 21

domain: (-pi/2, pi/2)
range: all real numbers

Question 22

law of sins

Answer 22

sina/a = sinb/b = sinc/c

Question 23

cases for law of sins

Answer 23

ASA, AAS, SSA (only sometimes)

Question 24

SSA (acute angle)

Answer 24

if a<h, no triangle
if a=h, one triangle
if a >= b, one triangle
if h<a<b, two triangles

Question 25

SSA (obtuse angle)

Answer 25

if a<=b, no triangle
if a>b, one triangle

Question 26

law of cosine

Answer 26

a²=b² + c² - 2bccosA

Question 27

cases for law of cosines

Answer 27

SAS, SSS

Question 28

Heron’s formula

Answer 28

A = √s(s-a)(s-b)(s-c)

Question 29

semi perimeter

Answer 29

(a + b + c)/2