Sine of non special angle | Trig identities and examples | Trigonometry | Khan Academy

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[Kuratius]

Question: Doesn't this just extend the amount of special angles that we can calculate without actually allowing us to calculate any arbitrary angle? Like for example 7.5 pi/12?

[SummerFrost]

I thought you can but not.
7π /12 = 105°

sin (105°) = sin (75°) = cos (15°)

Use special angles and half-angled trig identities,
cos ( θ ) = 2 cos ² ( θ/2) - 1

Let θ = 30°
cos ( 30° ) = 2 cos ² (15 °) - 1
(√3) / 2 = 2 [ cos (15°) ] ² - 1

Thus,
sin ( 7π/ 12)
= cos ( 15°)
= √ ［ (√3 + 2 ) / 4 ］
= √ ［ ( 2 √3 + 4 ) / 8］
= ( 1 + √3 ) / ( 2 √2 )
= ( √2 + √6 ) / 4

[That_One_Guy...]

i wanted to know how to calculate non special angle value of trig values (not the extension of the special angles, i mean like sin 55 or sin 21, etc) without taylor series

[putinscat]

Nice! Is there any way to just calculate sin(7.5 degrees) or any angle without using series? And would series be faster in this case?

[goose]

How do you find the Tangent or cosine of a non special angle?