Question

??

Answer 1

5a part I: you have the angle -pi/6

you can find an equivalent angle by adding 2pi to that

then look at the Unit circle for the appropriate cos value

Answer 2

adding -pi/6 + 2pi gives us 11pi/6

so you just need to find the value of cos(11pi/6)

Answer 3

still there?

Answer 4

(-pi/6)+2pi=11pi/6= ((3pi)/2)/2 , -1/2

Answer 5

sorry i was doing something

Answer 6

good but they only want the cos value so sqrt(3)/2

Answer 7

for part II you simply need to observe the values between 0 and pi to see which angle gives you a cos value of sqrt(3)/2

Answer 8

there's only one possibility, pi/6

Answer 9

okay so for b

Answer 10

find the hypotenuse using the pythagorean theorem

Answer 11

c=5

Answer 12

good

since arctan(4/3) is just another way to say theta, the expression becomes

sin(theta) = opposite/hypotenuse so find sin(theta)

Answer 13

what is sin(theta) equal to?

Answer 14

from the perspective of theta, 4 is the opposite side and 5 is the hypotenuse

making sin(theta) = ?

Answer 15

opposite/hypotenuse = 4/5

Answer 16

c is pretty straightforward, first it asks you for the value of cos(pi/2) which can be found w/ a calculator or w/ the unit circle

then it asks for a theta value between (-pi/2 and pi/2) where tan(theta) = 0

Answer 17

0

Answer 18

for part I

Answer 19

good, keep going

Answer 20

(0,1)

Answer 21

for part II what angle between -pi/2 and pi/2 does tan(theta) = 0

Answer 22

pi

Answer 23

pi is not between -pi/2 and pi/2

Answer 24

remember that tan(theta) = sin(theta)/cos(theta) so you should be looking for the theta between -pi/2 and pi/2 where sin(theta) = 0

Answer 25

(1,0)

Answer 26

we are looking for a theta value so what would the theta value for that point be?

Answer 27

pi/2

Answer 28

that's (0,1) not (1,0)

Answer 29

the angle theta would be 0 as well