find exact value of sin15 degrees?

Answer 1

15 degrees = pi/12

pi/12 = 4pi/12 - 3pi/12 = pi/3 - pi/4

sin(15) = sin(pi/12)
= sin(pi/3 - pi/4)
= sin(pi/3)cos(pi/4) - sin(pi/4)cos(pi/3)
= [sqrt(3)/2] [sqrt(2)/2] - [sqrt(2)/2] (1/2)
= sqrt(6)/4 - sqrt(2)/4
= [sqrt(6) - sqrt(2)]/4

Answer 2

You need to use your knowledge of the more familiar angle, 30 degrees, along with the identity sin(x/2) = sqrt((1 - cos(x))/2). cos(30) = sqrt(3)/2, an identity that you should know offhand. That means that sin(30/2) = sin(15) = sqrt((1 - cos(30))/2) = sqrt((1 - sqrt(3)/2)/2) = sqrt(1/2 - sqrt(3)/4). If you'd like to multiply everything inside the square root by 4, you could also state this as (1/2)*sqrt(2 - sqrt(3)).

Answer 3

we know cos 30 degrees = sqrt(3)/2

cos 2t = 1 - 2 sin^2 t

put t = 15 degrees

sqrt(3)/2 = 1-2 sin^2 15

sin ^2 15 degrees = (1-sqrt(3)/2)/2

sin 15 degrees = sqrt((1-sqrt(3)/2)/2)

Answer 4

sin(15)=sin(60-45)=sin(60) x cos(45) - sin(45) x cos(60)= 0.25882


this is a rule here use it
sin ( A + or - B ) = sinA x cos B + or - sinB x cosA

as A and B are known degrees and no need to calcuator

Answer 5

Use sin30 = 1/2 and the double angle formula for sine.

Answer 6

use excel or use your calculator.

=sin(15) = 0.65028784