Question

Find an exact value.

cos 165°

Answer 1

whats two number you can add to get 165? and those two number suppose to be on the unit circle

Answer 2

then use formula \[\large\rm cos(a+b)=\cos a \times \cos b - \sin a \times \sin b\]

Answer 3

90 & 75 ?

Answer 4

well 75 is not on the unit circle :/

Answer 5

120 + 45

Answer 6

30+135
40+120
225-60 for this u have to use cos(a-b)=cos a times cos b + sin a times sin b

Answer 7

perfect!

Answer 8

so \[\huge\rm cos(45+120)=\cos 45 \cos 120 - \sin 45 \sin 120\]

Answer 9

okay, i see. what do i do from there?

Answer 10

so \[\large\rm cos(45+120)=\cos 45 \cos 120 - \sin 45 \sin 120\]
now use the unit circle cor exact value of cos and sin
cos 45 =?
cos 120 =?
sin 45=?
sin 120 =?
plugin their exact values

Answer 11

cos 45 = (radical)2 / 2
cos 120 = -1/2
sin 45 = (radical) 2 /2
sin 120 = (radical) 3 /2

is that right?

Answer 12

\[\frac{ \sqrt{2} }{ 2 } \times \frac{ -1 }{ 2 } - \frac{ \sqrt{2} }{ 2 } \times \frac{ \sqrt{3} }{ 2}\]
solve

Answer 13

yes that's right