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zysi [14]
2 years ago
7

If the sine ratio is given, then how can sin 0/2 be determined?

Mathematics
1 answer:
pogonyaev2 years ago
8 0

Step-by-step explanation:

If you know, the sine. You must find the cos ratio, using the Pythagorean trig theorem.

Next, you use the half angle identity for sin

\sin( \frac{ \alpha }{2} )  =  \sqrt{ \frac{1   -  \cos(a) }{2} }

Example.

\sin( \alpha )  =  \frac{ \sqrt{3} }{2}

We must find

\sin( \frac{ \alpha }{2} )

First, use the Pythagorean identity

\sin {}^{2} ( \alpha )  +  \cos {}^{2} ( \alpha )  = 1

( \frac{ \sqrt{3} }{2} ) {}^{2}  +  \cos {}^{2} (a)  = 1

\frac{3}{4}  +  \cos {}^{2} (a)  = 1

\cos {}^{2} (a)  =   \frac{1}{4}

\cos( \alpha )  =  \frac{1}{2}

Now use the half angle identiy

\sin( \frac{ \alpha }{2} )  =  \sqrt{ \frac{1 -  \cos( \alpha ) }{2} }

=  \frac{ \sqrt{1 -  \frac{1}{2} } }{ \sqrt{2} }

=  \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} }

=  \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} }  \times  \frac{ \sqrt{2} }{ \sqrt{2} }  =  \frac{ \sqrt{1} }{ \sqrt{4} }  =  \frac{1}{2}

So the answer for our example is 1/2

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21. First, find the volume of the rectangular prism. V = HLW
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Add the two volumes together, the total volume is 850 cm^3. The fourth answer is correct.

22. The volume of a square pyramid is V = 1/3(S^2)(H), where S is the side length and H is the height.

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2800 = (1/3)(84)(S^2)
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100 = S^2
<span> 10 in = S, so we have a side length of 10 in, and the first answer is correct. </span>
3 0
3 years ago
Help me please will brainlist
Thepotemich [5.8K]

Answer:B

Step-by-step explanation:

18 is greater than >16

18> 8-8(-1)

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8 0
3 years ago
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The answer will be 33
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