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Cosine trouble

Recently I was studying work and energy chapter, i saw the formula for 'work done when a body moves at an angle in the direction of force, it was given as -

                       Work done = Force cos θ * distance moved by the body

The book is saying that according to the table of natural cosines....cos 60 deg = 0.5 But in exams we can't look up at the table or don't get time to draw any equilateral triangle etc, to calculate cosine of any angle, please help, isn't there any formula to take out the cosine of any angle, there must be one, because by the formula only the cosine of different angles must have been found out, and then the table must have been prepared. Please help and share your views.

Note by Sahba Hasan
2 years, 5 months ago

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Sadly, you'll have to memorize the values of cosine. Thankfully, they mostly ask the cosines of five angles, \( 0^\circ,30^\circ,45^\circ,60^\circ,90^\circ \)

You can use a table to memorize those.

\( \cos 0^\circ \)\( \cos 30^\circ \)\( \cos 45^\circ \)\( \cos 60^\circ \)\( \cos 90^\circ \)
\( \sqrt{\frac{4}{4}} \)\( \sqrt{\frac{3}{4}} \)\( \sqrt{\frac{2}{4}} \)\( \sqrt{\frac{1}{4}} \)\( \sqrt{\frac{0}{4}} \)
Siddhartha Srivastava · 2 years, 5 months ago

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@Siddhartha Srivastava Thank you, but that's sad that i have to memorize, but then how was this table created? Sahba Hasan · 2 years, 5 months ago

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Yes, you would have to learn the cosines, sines and tans of mostly 5 angles i.e. 0, 30 , 45, 60, 90 Shayan Khan · 2 years ago

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