Find the Exact Value of Cosine of 15 Degrees, cos(15)

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Find the Exact Value of Cosine of 15 Degrees, cos(15)

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...The nice thing about these kinds of Trig problems is that they can sometimes be solved in different ways with the same solution. In this case 60(deg)-45(deg)=15(deg) can also be applied, and then using the same formula cos(60-45)=... as The Math Sorcerer in the video... I like Trigonometry

jan-willemreens

The other fornula you can use is the half angle: cos(2x) = 2.cos^2(x) - 1, which yields cos(x) = sqrt((1+cos(2x))/2)
And the fun begins: cos^2(15d) = (1+cos(30d))/2, cos^2(15d) = (1+sqrt(3)/2)/2 = (2+sqrt(3))/4
And thus we have cos(15) = sqrt((2+sqrt(3))/2. Which is exactly the same thing as what you found, or what Wolfram Alpha gives: (1+sqrt(3))/(2.sqrt(2)).
And the beauty is this: 2+sqrt(3) = (1+sqrt(3))^2/2

Jonasz

Literally, the first 30 seconds of the video helped me

wesley

One can also use cos(2v) = 2cos^2(v) - 1 i.e. cos(15) = sqrt((cos(30)+1)/2) and cos(30) = sqrt(3) / 2

malawigw

Hey I m from India I love your channel can you make a detailed video on how to learn very very very very very very advanced maths love you

intrestingbiographies

You could simplify that even further by writing it as ( sqrt(2) * (sqrt(3) + 1) ) / 4. Really cool video though! Keep up the good work!

the_vultdweller

oh so thats why it's the only other angle that has a precise value we can calculate on a calculator

arthurbuffon

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