Очень срочно нужно!!! Помогите!. Created by id161. matematika-ru

Очень срочно нужно!!! Помогите!...

id161 @id161

August 2022 1 9 Report

Очень срочно нужно!!! Помогите!

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daraprelj

8. $sin\alpha = \frac{12}{13}$

α∈( $0; \frac{\pi }{2}$ )

cos α - ?

Из основного тригонометрического тождества sin²α+cos²α= 1 выразим cos α

cos α= √1-sin²α

Т.к. α∈( $0; \frac{\pi }{2}$ ), то cos положителен

$cos\alpha = \sqrt{1-(\frac{12}{13})^{2} } = \sqrt{\frac{169-144}{169} } = \sqrt{\frac{25}{169} } = \frac{5}{13}$

9. $2sin(x+\frac{\pi }{2} ) = 1$ | : 2

$sin(x+\frac{\pi }{2} ) = \frac{1}{2}$

$x+\frac{\pi }{2} = (-1)^{n}*arcsin \frac{1}{2} + \pi n$ , n∈Z

$x = (-1)^{n}*\frac{\pi }{6} - \frac{\pi }{2} + \pi n$ , n∈Z

10. $log_{2}(2-2x) = 2log_{2} 4$

$log_{2}(2-2x) = 2*2$

$log_{2}(2-2x) = 4$

$2-2x =2^{4}$

$2(1-x) = 16$ | : 2

1 - x = 8

- x = 8 - 1

x = -7

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