Question

Write the expression as either the sine, cosine, or tangent of a single angle.

cosine of pi divided by three times cosine of pi divided by five plus sine of pi divided by three times sine of pi divided by five.

Answer 1

cos (pi/3) cos(pi/5) + sin(pi/3)sin(pi/5)

Answer 2

when I solve it I get 0.913545458 but now I do not know what angle it can be for sin , cos ,tan

Answer 3

you use the identity
cos(A-B) = cosAcosB + sinAsinB

Answer 4

how do I do that

Answer 5

let A = pi/3 and B = pi/5
- do you see how we can write it as the cos of one angle?

( work from right to left)

Answer 6

so cos(pi/3-pi/5) = cospi/3cospi/5 + sinpi/3sinpi/5

Answer 7

right

Answer 8

on the right I get 0.913545458

Answer 9

and on the left the same

Answer 10

- yoou dont need to find the numerical values you on;y need to write it as a cosine

cos (pi/3 - pi/5) = cos (2pi/15)

Answer 11

wait so is that all I have to write ?

Answer 12

or do I have to continue solving?

Answer 13

no thats all
you have written it as the cosine of one angle

Answer 14

oh ! okay okay , thank you so much for your help

Answer 15

yw

Answer 16

the fact that you get 0.9135454 on both sides does serve as a check though - that we have the right answer