SOLUTION: What is the exact value of sin(-7pi/12) and how do you find it?

Question 1063062: What is the exact value of sin(-7pi/12) and how do you find it?
Found 3 solutions by rothauserc, ikleyn, math_helper:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
pi is 180 degrees
:
180 / 12 = 15 and -7 * 15 = -105
:
360 + (-105) = 255
:
255 is in the third quadrant where the sin is negative
:
sin(255) = −0.9659
:

Answer by ikleyn(52793)   (Show Source): You can put this solution on YOUR website!
.

Exact value of sin(-7pi/12) is = = To find , use the formula of half argument for cosines (see the lesson Trigonometric functions of half argument in this site): cos^2(15�) = (1+cos(30�)/2 = = . Hence, cos(15�) = . Thus = .

See the lesson
    - Trigonometric functions of half argument - Examples
in this site.
-------------------------

Regarding the solution by the tutor "math_helper" for this problem, I want to notice that this solution consists and coincides with my:

= .

Everybody who squares both sides can check it and convince himself or herself.

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
(because sin(-a) = -sin(a))
=
=
�
Use sin(a+b) = sin(a)cos(b) + cos(a)sin(b) :
--
=
�
Use these 3 facts:

�
Continuing�
=
=
=

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