Problems Set at an Oral Examination.
Compare the following numbers.
(a) sin 3 and cos 3; (b) $\sqrt[3]{3} a n d \sqrt{2} .$

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Solution

$3$ in radians means approxly $3 \times 57$ degrees $= 171$ degrees

therefore $sin 3 > cos 3$ since $cos$ is -ve

$3^{1 / 3} = 1.4422495$
and $2^{1 / 2} = 1.414$

therefore $3^{1 / 3}$ is greater

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Similar questions

3 < π < 4.

A = 4 + \frac{5}{8} + \frac{6}{8^{2}} + \frac{3}{8^{3}} + \frac{7}{8^{4}} a n d B = 4 + \frac{5}{8} + \frac{5}{8^{2}} + \frac{7}{8^{3}} + \frac{6}{8^{4}} .

x + 2 x^{2} + 3 x^{3} + . . . + n x^{n} .

y = s i n | 2 x | .

y = l o g_{| s i n x |} (1 / 2) .

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