Question

cos(pi)/16cos(3pi)/16-sin(pi)/16sin(3pi)/16 find the exact value of the expression

Answer 1

Can you write it with brace's or use openstudy's formula template?

Answer 2

*brackets

Answer 3

\[\cos \frac{ \pi }{ 16 }\cos \frac{ 3\pi }{ 16? }-\sin \frac{ \pi }{ 16}\sin \frac{ 3\pi }{ ?16 }\]

Answer 4

\[\frac{ 1 }{ \sqrt{2} }\]

Answer 5

can you show the steps please so that I can learn it

Answer 6

You can use a calculator..can you not use one?

cos(33.75 degrees)cos(11.25 degrees) = 0.81549

sin(33.75 degrees)sin(11.25 degrees) = 0.10839

0.81549 - 0.10839 is about equal to 1/sqrt(2)

Answer 7

There's another way to do it

Answer 8

I converted pi/16 and 3pi/16 into degrees, just because it's easier

let angle A = pi/16
let angle B = 3pi/16

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

cos(A+B) = cos( (pi/16) + (3pi/16) ) = 1/sqrt(2)

Answer 9

oh ok
thanks

Answer 10

(pi/16)+(3pi/16) = 45 degrees

cos(45 degrees) = 1/sqrt(2)