SOLUTION: Use the sum or difference identities to find the exact value of the trigonometric function. sin(735 degrees)

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Question 1032964: Use the sum or difference identities to find the exact value of the trigonometric function.
sin(735 degrees)
Found 3 solutions by Alan3354, ikleyn, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the sum or difference identities to find the exact value of the trigonometric function.
sin(735 degrees)
------------
= sin(15) degrees
---------
Look up half angle formulas on Wikipedia.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the sum or difference identities to find the exact value of the trigonometric function.
sin(735 degrees)
~~~~~~~~~~~~~~~~~~~~~~~~ 

sin(735°) = sin(720° + 15°) = sin(15°),   since sine is periodical function with the period of 360°.

sin(15°) = sqrt%28%281-cos%2830%5Eo%29%29%2F2%29 =   (formula of half argument for sine, see the lesson  Trigonometric functions of half argument  in this site)

= sqrt%28%281+-+sqrt%283%29%2F2%29%2F2%29 = sqrt%28%282-sqrt%283%29%29%2F4%29 = sqrt%282-sqrt%283%29%29%2F2.


See also the lesson  Trigonometric functions of half argument - Examples,  Example 2.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use the sum or difference identities to find the exact value of the trigonometric function.
sin(735 degrees)
One of the terminal angles of 735%5Eo is 735 - 2(360), or 735 - 720 = 15%5Eo

Difference of two angles' identity associated with 15%5Eo is: 

sin+%2845%5Eo%29+=+sqrt%282%29%2F2

cos+%2830%5Eo%29+=+sqrt%283%29%2F2

cos+%2845%5Eo%29+=+sqrt%282%29%2F2

sin+%2830%5Eo%29+=+1%2F2