Question

find the exact value of the following? sin195

Answer 1

\[\frac{ (-\sqrt{6} + \sqrt{2})}{ 4 }\]

Answer 2

i got -1/2\[-1/2\sqrt{2-\sqrt{3}}\]

Answer 3

\[\sqrt{(1-\cos(30))/2} = \sqrt{1/2(2/2 - \sqrt{3}/2}\]

Answer 4

you use the half angle formula

Answer 5

my teacher provided me with this sin20=cos^20(theta)*cos(theta) but i dont understand what do i do with it do i plug in the 195 instead?

Answer 6

hmm you dont have any instructions? say something like prove the identity because sin2theta = 2sincos

Answer 7

nope thats all that it says

Answer 8

well the exact value of sin(195) is \[-1/2\sqrt{2-\sqrt{3}}\]

Answer 9

wait nvm i read the half angle identity
oops sorry

Answer 10

using the half angle formula we double the angle value of 195 which comes to 390

Answer 11

ok

Answer 12

since 390 is coterminal with 30 with use the value of cos(30) in the formula

Answer 13

the formula is \[\sqrt{(1-\cos(\theta))/2}\]

Answer 14

the cos of 30 is \[\sqrt{3/}2\]

Answer 15

what do you mean by coterminal shouldnt the 30 be negative or something

Answer 16

im just trying to understand it

Answer 17

so the formula becomes \[\sqrt{(1-\sqrt{3}/2)/2}\]

Answer 18

coterminal just means they are at the same spot on the unit circle

Answer 19

since double 195 is 390 that means it goes all the way 360 degrees and then there is another 30 degrees

Answer 20

ok

Answer 21

your angle went all the way around + 30 so its at pi/6

Answer 22

alright i got that part

Answer 23

so the cosine of 390 and 30 is the same

Answer 24

since your angle is 195 we use the half angle formula

Answer 25

ok

Answer 26

because 195 is hard to get an exact number for we double it which gives a good number that lands on 30degrees and just divide that by 2

Answer 27

but the complete formula is \[\sqrt{(1-\cos(x))/2}\]

Answer 28

wait so do i divide 30? by 2 or what do i divide?

Answer 29

let me see if i can figure out how to put fractions into the equations im kinda new to openstudy

Answer 30

ok thanks and i am to

Answer 31

ill just draw it

Answer 32

ok