Question

use the angle identity to find the exact value of each:
cos 105 degrees and
sin 195 degrees

Answer 1

@ikram002p do you know how to solve this question

Answer 2

for the first one, this is how i solved it, '
cos105=cos(60+45)=cos60*cos45+sin60*sin45
=sqrt(1)/2*sqrt(2)/2+sqrt(3)/2*sqrt(2)
=sqrt(2)+sqrt(6)/4

Answer 3

105=45+60
so
cos 105=cos( 45+60)=cos 60 cos 45 - sin 60 sin 45

Answer 4

yeah ur correct

Answer 5

but its wrong, do we not square

Answer 6

1/2

Answer 7

because i'm evaluating my functions incorrectly

Answer 8

one sec there is negative sighn not positive

Answer 9

why

Answer 10

if something is not squared and something is, we cannot add it

Answer 11

cos (A+B)= cos A cos B - sin A sin B

Answer 12

then it would be 1/2*sqrt(2)/2-sqrt(3)/2*sqrt(2)/2

Answer 13

how would we add it up

Answer 14

1/4 sqrt 2 - sqrt 6 /4 = (sqrt 2- sqrt 6)/4
leave it like this

Answer 15

we do not subtract it

Answer 16

what about sin 195

Answer 17

this is how i solved it
2) Sin195=Sin(150+45)=Sin150*Cos45+Sin150*cos45
=1/2*sqrt(2)/2+1/2*sqrt(2)/2
=sqrt(2)+sqrt(2)/4

Answer 18

nope
sin (A+B)= sin Acos B + cos A sin B

Answer 19

cos 75 degrees
cos75=cos(45+30)=cos45*cos30-sin45*sin30
=sqrt(2)/2*sqrt(3)/2+sqrt(2)/2*1/2
=sqrt(6)+sqrt(2)/4 (EXACT VALUE)

Answer 20

thats right

Answer 21

ok 1 sec

Answer 22

sin105=sin(90+45)=sin90*cos45+Sin90+cos45
=1/1*sqrt(2)/2+1/1*sqrt(2)/2
=sqrt(2)+sqrt(2)/2 (EXACT VALUE)

Answer 23

nope

Answer 24

where is my fault

Answer 25

sin 1505= sin 60 cos 45+cos 60 sin 45

Answer 26

oh

Answer 27

) Show sin 4θ = 4sin θ cos θ cos 2 θ
Sin2 θ=2sin(2 θ)cos(2 θ)
(4sin xcos x)cos2 x
=2(2sin xcos x)cos2 x
=2sin2 xcos2 x
Put 2x= θ
=2sin θ cos θ
=sin 2 θ , θ=2x
=sin4x QED

Answer 28

i solved sin 105

Answer 29

@ikram002p would sin theta equation above be correct

Answer 30

i dnt understand ur question ?!

Answer 31

Show sin 4θ = 4sin θ cos θ cos 2 θ

Answer 32

i solved it above

Answer 33

sin 4θ = 4sin θ cos θ cos 2 θ
sin 4θ =(sin 2 θ +2 θ)
=sin 2 θ cos 2 θ+sin 2 θ cos 2 θ
=2 sin 2 θ cos 2 θ
=2(2 sin θ cos θ)cos 2 θ
=4 sin θ cosθ cos 2 θ

Answer 34

this is how u show it , btw i coudnt go through ur steps