How do I find the exact value of sin15 deg. ????

Answer 1

sin (45 - 30)°
sin 45° cos 30° - cos 45° sin 30°
(1/√2) (√3/2) - (1/√2) (1/2)
( √3 - 1) / (2√2)

Answer 2

15 is 45 - 30 so use the formula for sin (a-b)

sin (45 - 30 ) = sin 45 cos 30 - sin 30 cos 45

= (√2 / 2)(√3 / 2) - 1/2 (√2 / 2)

= √6 - √2 all over 4

Answer 3

You use the half-angle formula: sin(theta/2) = +/- sqrt((1-cos(theta))/2). 30 degrees is one of the basic angles that most trig teachers expect you to memorize; its cosine is sqrt(3)/2. So sin(15) = sin(30/2) = +/- sqrt(1-sqrt(3)/2)/2) = +/- sqrt(1/2 - sqrt(3)/4).

To get the sign, you just have to use some common sense. 15 degrees is in the first quadrant of the unit circle, so its sine and cosine should both be positive. Since a square root is always positive, we know that sin(15) = sqrt(1/2 - sqrt(3)/4).

I'll bet there's some way to simplify that, but I can't think what it could be.

Answer 4

sin15° = sin(45° - 30°)
=sin(45°)cos(30°) - cos(45°)sin(30°)
= [1 / √2][(√3) / 2] - [1 / √2] [1/2]

=[√6 - √2] / 4



http://rbmix.com/math/trignometry/trig.php

Answer 5

sin 30 = .5 and cos 30 = sqrt(3)/2
Now use the half angle formula to find sin 15

Answer 6

Press 15 (make sure the mode is deg) on your calculator and then press SIN.

Answer 7

Use the calculator in Windows. Go to the Start menu and go to Run. In the box type

calc

Set the option to scientific

Answer 8

sin(x/2) = sqrt{[1-cos(x)]/2}
sin(30/2) = sqrt{[1-cos(30)]/2}
cos(30) = sqrt(3)/2

sin(15) = sqrt{[2-sqrt(3)]/4}

I like the other answers better ...
sin(45-30) = sin45 cos30 - cos45 sin30

Answer 9

Use the half angle trig identity.
sin (theta/2) = √((1-cos(theta)/2)

and use cos(30) = √(3)/2

Answer 10

sin(15) = sin(45-30)

sin(A-B) = sin(A)cos(B)- cos(A)sin(B)
So:

sin(45)cos(30)-cos(45)sin(30) =
(1/6)^(1/2) - (1/2)(.5)^(1/2)