Mathematics: What is the exact value of sin(105°)?ANSWER - D) sqrt(2 + sqrt3)/2

What is the exact value of sin(105°)?ANSWER - D) - id10510594330, winstonbendariovvygn

Ответ:

abelgutierrez370

17.03.2022

Mathematics

$\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}$

Step-by-step explanation:

We can use the following trigonometrical identity:

$\sin (\alpha - \beta) = \sin \alpha \cdot \cos \beta - \cos \alpha \cdot \sin \beta$ (1)

Where $\alpha$ , $\beta$ are angles, measured in sexagesimal degrees.

If we know that $\alpha = 135^{\circ}$ and $\beta = 30^{\circ}$ , then the value of the given function is:

$\sin 105^{\circ} = \sin 135^{\circ}\cdot \cos 30^{\circ} - \cos 135^{\circ}\cdot \sin 30^{\circ}$

$\sin 105^{\circ} = \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{\sqrt{3}}{2}\right)-\left(-\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2}\right)$

$\sin 105^{\circ} = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}$

$\sin 105^{\circ} = \sqrt{\frac{6}{16} }+\sqrt{\frac{2}{16} }$

$\sin 105^{\circ} = \sqrt{\frac{3}{8} }+\sqrt{\frac{1}{8} }$

$\sin 105^{\circ} = \frac{\sqrt{3}+1}{2\cdot \sqrt{2}}$

$\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}$

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Ответ:

20jhutchinson

18.12.2021

Mathematics

answer:

C, John Proctor

Step-by-step explanation:

That's part of how he justifies confessing when he first considers doing it. Confessing to witchcraft, something he knows is false, is something he considers evil. But, hey...he cheated on his wife. He's already evil. Might as well do something else.

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What is the exact value of sin(105°)?

ANSWER - D) sqrt(2 + sqrt3)/2

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