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2 years ago

Help with Trigonometric identities

Mathematics

1 answer:

Gre4nikov [31]2 years ago

3 0

Answer:

Option 2

Step-by-step explanation:

Since theta is in the third quadrant, the sine of theta is negative.

By the Pythagorean identity,

$\sin \theta=-\frac{\sqrt{105}}{13}$

So, using the double angle formula for sine, we get that

$\sin 2\theta=\frac{16\sqrt{105}}{169}$

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Find the value of x and y so that both proportions will be correct:

andrew11 [14]

The values of x and y are 0.2 and 0.4 respectively.

Explanation

The given proportions are.....

$x: 1\frac{2}{3}=y: 3\frac{1}{3}$ and $y:1.5=0.2:0.75$

From the second proportion, we will get....

$y:1.5=0.2:0.75\\ \\ \frac{y}{1.5}=\frac{0.2}{0.75} \\ \\ 0.75y=0.2*1.5\\ \\ 0.75y=0.3\\ \\ y=\frac{0.3}{0.75}=0.4$

Now, we will plug this $y=0.4$ into the first proportion. So we will get....

$x: 1\frac{2}{3}=y: 3\frac{1}{3}\\ \\ x: \frac{5}{3}=0.4:\frac{10}{3} \\ \\ \frac{x}{\frac{5}{3}}= \frac{0.4}{\frac{10}{3}}\\ \\ \frac{3x}{5}=\frac{1.2}{10}\\ \\ 30x=6\\ \\ x= \frac{6}{30}=0.2$

So, the values of x and y are 0.2 and 0.4 respectively.

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Step-by-step explanation:

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Step-by-step explanation:

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