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3 years ago

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What are two ratio that are equivalent to 15:20

2 answers:

ziro4ka [17]3 years ago

8 0

3:4 is the equivalent ratio

qwelly [4]3 years ago

7 0

Hey there!

$15:20$

$\frac{15}{5} = 3 \\ \\ \frac{20}{5} = 4$

Answer: $3:4$

Good luck on your assignment and enjoy your day!

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Answer:

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$x$ is in quadrant II, so $\sin x>0$ .

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Then with the conditions determined above, we get

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and

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Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

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$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

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$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

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$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

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