How do you convert 0.991 into a fraction

Mathematics

2 answers:

inn [45]3 years ago

7 0

991 / 1000 . The decimal is in the thousandths place, so you put it over one thousand

LekaFEV [45]3 years ago

6 0

You divide 0.991 by 100.

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Read 2 more answers

Find the exact value of tan(165°) using a difference of two angles

Katyanochek1 [597]

Answer: $-2+\sqrt{3}$

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Work Shown:

Apply the following trig identity

$\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\$

Now let's rationalize the denominator

$\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\$

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As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.

Or you can note how

$\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949$