Let a = cos 1 ° and b = sin 1 ° . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,

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Let a = cos 1 &#176; and b = sin 1 &#176; . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,

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Correct answer: C. both a and b are algebraic

We have, a = cos 1 &#176; and b = sin 1 &#176; cos x + i sin x n = cos n x + i sin n x cos x - i sin x n = cos n x - i sin n x &#8658; 2 cos n x = cos x + i sin x n + cos x - i sin x n Put x = 1 &#176; and n = 60 = 2 cos 60 &#176; = 2 cos 60 1 &#176; + C 2 60 cos 58 1 &#176; i 2 sin 2 1 &#176; &#8230; . Change all sin 1 &#176; to cos 1 &#176; using the identity cos 2 1 &#176; = 1 - sin 2 1 &#176; equation with root cos 1 &#176; so it is algebraic. Similarly, for b = sin 1 &#176;

Let a = cos 1 ° and b = sin 1 ° . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,

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More from Complex Number

Let a = cos 1 &#176; and b = sin 1 &#176; . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,

Options

Correct answer

Step-by-step solution

More from Complex Number

Let a = cos 1 ° and b = sin 1 ° . We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,