Question

sin 35° in fraction form

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Answer 1

Given:

sin 35°

To find:

The fractional form

Solution:

sin 35°=sin 30° cos 5°+sin 5° cos 30°

We already know the values of sin 30° and cos 30°, so we put the values to get,

sin 35°=$\frac{1}{2}$cos 5°+$\frac{\sqrt{3} }{2}$sin 5°

Now, since 5°=$\frac{\pi }{36}$ which is a relatively small angle, we can approximate that

sin x≈x and cos x≈1

So, now we again put the values in the equation to get,

sin 35°=$\frac{1}{2}+(\frac{\sqrt{3} }{2})(\frac{\pi }{36} )$

⇒sin 35° ≈$\frac{1}{2}+(\frac{22}{7} )(\frac{1}{36} )(\frac{1}{2})(\frac{7}{4} )$

⇒sin 35°=$\frac{1}{2}+\frac{11}{144}$

⇒sin 35°=$\frac{83}{144}$

Hence, sin 35° is $\frac{83}{144}$.