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Elina [12.6K]
3 years ago
12

Write a number sentence to represent the sum modeled on the number line. In two or more complete sentences, explain your reasoni

ng.

Mathematics
1 answer:
Afina-wow [57]3 years ago
4 0

Answer:

0 + (-2.5) + 5

Step-by-step explanation:

from 0 to -2.5 then to 5 so add 0 + (-2.5) + 5

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scZoUnD [109]

Right away, we know that

\cos\beta=\dfrac{16}{20}=\dfrac45

which means

\sin\beta=\sqrt{1-\cos^2\beta}=\dfrac35

Then

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\sin\beta=\sin2\left(\dfrac\beta2\right)=2\sin\dfrac\beta2\cos\dfrac\beta2

Let x=\cos\dfrac\beta2 and y=\sin\dfrac\beta2. Then

\begin{cases}\dfrac45=x^2-y^2\\\\\dfrac35=2xy\end{cases}\implies\begin{cases}\cos\dfrac\beta2=\dfrac3{\sqrt{10}}\\\\\sin\dfrac\beta2=\dfrac1{\sqrt{10}}\end{cases}

from which we find

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You can use the same ideas above to find the trig ratios for \dfrac\alpha2, starting from the given fact that \sin\alpha=\dfrac{16}{20}=\dfrac45.

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