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drago12

drago12

15.11.2020 •

Mathematics

Find the equivalent function of sin(180+x)

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Ответ:

jonnys412

08.02.2022

The equivalent function of $sin\left(180^{\circ }+x\right)$ will be: $-\sin \left(x\right)$

i.e.

$\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)$

Step-by-step explanation:

Considering the function

$sin\left(180^{\circ }+x\right)$

Solving

$sin\left(180^{\circ }+x\right)$

Using the angle sum identity:

$\sin \left(s+t\right)=\sin \left(s\right)\cos \left(t\right)+\cos \left(s\right)\sin \left(t\right)$

$=\sin \left(180^{\circ \:}\right)\cos \left(x\right)+\cos \left(180^{\circ \:}\right)\sin \left(x\right)$

as

$\cos \left(180^{\circ \:}\right)=\left(-1\right)$

$\sin \left(180^{\circ \:}\right)=0$

so

$=0\cdot \:\cos \:\left(x\right)+\left(-1\right)\cdot \:\sin \:\left(x\right)$

$=0\cdot \cos \left(x\right)-1\cdot \sin \left(x\right)$

$=0-1\cdot \sin \left(x\right)$

$=0-\sin \left(x\right)$

$=-\sin \left(x\right)$

So, the equivalent function of $sin\left(180^{\circ }+x\right)$ will be: $-\sin \left(x\right)$

Therefore:

$\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)$

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Ответ:

granniejo

06.02.2022

Yes, the slope of both lines is 0.5, which means the lines really are parallel. they never intersect, so there is no point that lies on both lines, and no solution to the system. micaela is trying to find the number of possible solutions for a system of two linear equations.

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