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Novay_Z [31]
3 years ago
5

Express sin(3theta) in terms of sin (theta)

Mathematics
2 answers:
BigorU [14]3 years ago
7 0
3∅ can be rewritten as (2∅+∅)
sin(3∅) = sin(2∅ + ∅<span>)
Opening brackets on the right hand side;
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This simplifies to;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3<span>∅</span>
tamaranim1 [39]3 years ago
5 0

First of all:-

3∅ can be called (2∅+∅)
so, sin(3∅) = sin(2∅ + ∅<span>)
Open brackets on the RHS (right hand side)
 = sin2</span>∅ cos ∅ + cos2∅sin<span>∅
</span><span>This is simplified into;
 = 2sin</span>∅cos^2∅ + sin∅ (1- 2sin^2∅<span>)
 = sin</span>∅ (2cos^2∅ + 1 - 2sin^2∅<span>)
 = sin</span>∅ (2(1 - sin^2∅) +1-2sin^2∅<span>)
 = 3sin</span>∅ - 4sin^3∅

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  13 units from 20 could either be 33 or 7; 15 units from -8 could either be 7 or 23.Since 7 satisfy both of the above requirements, Sarah's favorite number is 7. (You could show your work using a number line)
 
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7 0
3 years ago
Read 2 more answers
The probability that a single radar station will detect an enemy plane is 0.65. (a) How many such stations are required to be 98
Inga [223]

Answer:

4 stations

Step-by-step explanation:

If we need to be at least 98% certain that an enemy plane flying over will be detected by at least one station, we must ensure that there is at most a 2% chance that no radar stations detect the plane.

The probability that a single radar station does not detect the plane is 0.35.

For n radar stations:

P=0.02=0.35^n\\n=\frac{log(0.02)}{log(0.35)}\\n=3.73

Rounding up to the next whole station, at least 4 stations are needed.

4 0
3 years ago
What is the slope of a line that contains the points (5, -3) and (7, 3)? *
Allisa [31]

Slope formula: y2-y1/x-x1

We can use the given points to solve.

3-(-3)/7-5

6/2

3

Best of Luck!

4 0
3 years ago
Trevor is racing his dirt bike at about 30 miles per hour. If he keep a up this rate for an hour and a half, how many miles will
Free_Kalibri [48]

Answer: 45 miles


Step-by-step explanation:

Since Trevor rides 30 mph and does this for 1.5 hours, multiply 30 by 1.5


30 * 1.5 = 45

3 0
3 years ago
2. Similar pyramids have heights 12 cm and 20 cm. The volume of the larger pyramid is 8192 cm3. Determine each of the following,
Keith_Richards [23]
We know that

[volume of a <span>pyramid]=[area of the base]*h/3

</span><span>a) The scale factor of the smaller pyramid to the larger pyramid in simplest form
</span><span>
12/20----------> 3/5
the answer Part a) is 3/5

</span><span>(b) The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid

[</span>The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid]--------> (3/5)²------> 9/25------> 0.36

[volume of a larger pyramid]=8192 cm³
h=20 cm
so
[8192]=[area of the base larger pyramid]*20/3
[area of the base larger pyramid]=8192*3/20------> 1228.80 cm²<span>

</span>[area of the base smaller pyramid]=(3/5)²*1228.80-----> 442.37 cm²

The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid-----------> 442.37/1228.8--------> 0.36
0.36--------> is equal to (3/5)²

the answer part b) is 0.36  

<span>(c) Ratio of the volume of the smaller pyramid to the larger
</span>
[Ratio of the volume of the smaller pyramid to the larger]=(3/5)³---> 27/125
27/125------> 0.216

the answer Part c) is 0.216

<span>(d) The volume of the smaller pyramid

[</span>The volume of the smaller pyramid]=0.216*8192------> 1769.47 cm³
<span>
the answer part c) is </span>1769.47 cm³<span>



</span>

8 0
3 years ago
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