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2 years ago

PLEASE HELP Trig Idenities

Mathematics

1 answer:

kari74 [83]2 years ago

4 0

$\dfrac{\sin(A+B)}{\sin(A-B)}=\dfrac{\sin A\cos B+\cos A\sin B}{\sin A\cos B-\cos A\sin B}$

Divide through all terms by $\cos A\cos B$ . Then, for instance, the first term in the numerator becomes

$\dfrac{\sin A\cos B}{\cos A\cos B}=\dfrac{\sin A}{\cos A}=\tan A$

All other terms reduce similarly, giving the final product

$\dfrac{\tan A+\tan B}{\tan A-\tan B}$

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The function

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... y' = -1/x²

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How is the graph of the parent quadratic function transformed to produce the graph of y = negative (2 x + 6) squared + 3?

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The first child function would be

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The second child function would be

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We added 6 to the input of the function: we have

$h(x)=g(x+6)$

This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.

The third child function would be

$l(x)=-(2x+6)^2$

We changed the sign of the previous function (i.e. we multiplied it by -1): we have

$l(x)=-h(x)$

This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.

The fourth child function would be

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We added 3 to previous function: we have

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Recap

Starting from the parent function $y=x^2$ , we have to:

Compress the graph horizontall, with scale factor 2;
Translate the graph 6 units to the left;
Reflect the graph across the x axis;
Translate the graph 3 units up

Note that the order is important!

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