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JulijaS [17]
3 years ago
10

Find each quotient.

Mathematics
1 answer:
Pani-rosa [81]3 years ago
8 0

Answer:

123-98248294

4380583058903

3095804305394580

-0

Step-by-step explanation:

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100 and 110. 

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given: sin theta= 2/3 and theta is in the second quadrant; evaluate the following expression. sin2theta
andre [41]

The value of \sin(2\theta) is -\frac {-4\sqrt 3 }9

<h3>Sine ratio </h3>

The sine ratio is given as:

\sin(\theta) = \frac23

<h3>Trigonometry</h3>

In trigonometry, we have the following ratio

\sin^2(\theta) + \cos^2(\theta) = 1

Substitute \sin(\theta) = \frac23 in the above equation

\frac 23 + \cos^2(\theta) = 1

Collect like terms

\cos^2(\theta) = 1 -\frac 23

Evaluate

\cos^2(\theta) =\frac 13

Take square roots

\cos(\theta) =\pm\frac 1{\sqrt 3 }

Rationalize

\cos(\theta) =\pm\frac {\sqrt 3 }3

From the question, \theta is in the second quadrant, and cosine is negative.

So, we have:

\cos(\theta) =-\frac {\sqrt 3 }3

In trigonometry, we have:

\sin(2\theta) = 2\sin(\theta)\cos(\theta)

So, we have:

\sin(2\theta) = 2\times \frac 23 \times -\frac {\sqrt 3 }3

\sin(2\theta) =  -\frac {-4\sqrt 3 }9

Hence, the value of \sin(2\theta) is -\frac {-4\sqrt 3 }9

Read more about trigonometry ratios at:

brainly.com/question/10417664

7 0
2 years ago
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