If given the values of cos 2 and cos 3, sin 2 and sin 3, which of the following can be found arithmetically?

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If given the values of cos 2 and cos 3, sin 2 and sin 3, which of the following can be found arithmetically?

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Answer 1 · 2018-05-30T10:37:05

All of them

Explanation:

First

$cos (1) = cos (3 - 2)$ $cos(1) = cos(3-2)$ , and

$cos (a - b) = sin (a) sin (b) + cos (a) cos (b)$ $cos(a-b) = sin(a) sin(b) + cos(a) cos(b)$

which are all known.

Second

$cos (5) = cos (3 + 2)$ $cos(5) = cos(3+2)$ , and

$cos (a + b) = cos (a) cos (b) - sin (a) sin (b)$ $cos(a+b) = cos(a) cos(b) - sin(a) sin(b)$

which are all known.

Third

$sin (- 1) = sin (2 - 3)$ $sin(-1)=sin(2-3)$ , and

$sin (a - b) = sin (a) cos (b) - cos (a) sin (b)$ $sin(a-b) = sin(a) cos(b) - cos(a) sin(b)$

which are all known.

Fourth

This is the same as point $2$ $2$ , with $a = π$ $a=pi$ and $b = 2$ $b=2$ .

Fifth one: yes

$tan (4) = \frac{sin (4)}{cos (4)} = \frac{sin (2 + 2)}{cos (2 + 2)}$ $tan(4) = \frac{sin(4)}{cos(4)} = \frac{sin(2+2)}{cos(2+2)}$

And find $sin (4)$ $sin(4)$ and $cos (4)$ $cos(4)$ using again the formulas for $sin (a + b)$ $sin(a+b)$ and $cos (a + b)$ $cos(a+b)$ plugging $a = b = 2$ $a=b=2$ .

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If given the values of cos 2 and cos 3, sin 2 and sin 3, which of the following can be found arithmetically?

1 Answer

Explanation:

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