Question

use the sum/difference identities to evaluate exactly
cos 105 degree
Help plzz :(

Answer 1

105 = 60 + 45

Answer 2

105= 60+45
do you know
cos(A+B)= ?

Answer 3

cos(1/2+\[\sqrt{2}/2\])

Answer 4

there is a formula for the cosine of the sum of two angles
cos(A+B)= cos(A)cos(B) - sin(A)sin(B)

in your problem, A=60 and B=45
can you finish?

Answer 5

See http://www.intmath.com/analytic-trigonometry/2-sum-difference-angles.php

Answer 6

\[1/2*\sqrt{2}/2+\sqrt{3}/2*\sqrt{2}/2\]

Answer 7

now simplify

Answer 8

\[1/\sqrt{2}\]

Answer 9

but notice the two terms are subtracted (not added)

Answer 10

[-1/\sqrt{2}\]

Answer 11

you should start with
\[ \frac{1}{2}\cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \frac{\sqrt{2}}{2} \]

Answer 12

\[\sqrt{2}/4-\sqrt{6}/4\]

Answer 13

yes, or (which is the same thing)
\[ \frac{\sqrt{2}-\sqrt{6}}{4} \]
or
\[ \frac{\sqrt{2}(1-\sqrt{3})}{4}\]

they all evaluate to the same number. You can use a calculator and see cos(150 deg) = -0.258819...

Answer 14

* cos(105)= -0.258819...

Answer 15

thanks

Answer 16

yw