Question

Find the exact value of cos165 degrees

Answer 1

hi what are you choices

Answer 2

I don't have any lol

Answer 3

ok

Answer 4

Here use this cosine calcualtor http://rapidtables.com/calc/math/Cos_Calculator.htm

Answer 5

do you mean the cosine of 165 degrees?

Answer 6

Then -(√ (3) + 1)√ (2) / 4

Answer 7

ohhhh. okay thank you. and I cant use a calc but thanks

Answer 8

got Unit circle?

Answer 9

Find the exact value of cos165 degrees

Have you considered using the addition formula for the cosine function?
Note that cos 75 = cos (45 + 30) = cos 45 cos 30 - sin 45 sin 30. Think about this.
How could you use this juicy tidbit to solve the problem at hand?

Answer 10

\(\bf 165=120+45\qquad thus\qquad cos(165^o)\iff cos(120^o+45^o)
\\ \quad \\
recall \implies cos({\color{brown}{ \alpha}} + {\color{blue}{ \beta}})= cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}})- sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})
\\ \quad \\
cos({\color{brown}{ 120^o}})cos({\color{blue}{ 45^o}})-sin({\color{brown}{ 120^o}})sin({\color{blue}{ 45^o}})\)

Answer 11

yeah thanks guys I understand. the book gives me a formula but I'm dumb and didnt check. Thanks though

Answer 12

This is an excellent approach. Note that both 120 and 45 degrees are "special angles."
What's special about them?

Answer 13

They have values from the unit circle...
i guess