$sin \alpha =\sqrt{\frac{1-cos2\alpha }{2} } \\put~ \alpha =\frac{\pi }{8} \\2\alpha =\frac{\pi }{4} \\cos 2\alpha =cos \frac{\pi }{4}=\frac{1}{\sqrt{2} } \\\\sin(\pi/8)=\sqrt{\frac{1-\frac{1}{\sqrt{2} } }{2}} =\sqrt{\frac{\sqrt{2}-1 }{2\sqrt{2} }$

6 sin 3 \theta+6 sin \theta

$6 sin 3 \alpha +6 sin\alpha =6(sin 3\alpha +sin \alpha )\\=6 *2sin \frac{3\alpha+\alpha }{2} cos \frac{3\alpha-\alpha }{2} \\=12 sin 2\alpha cos \alpha$

please change α to \theta

5 0

3 years ago

12 23 17 20 14 14 18 16 17 18 18 mean median mode round to the rarest tenth

Vaselesa [24]

The mean is the average. To find this, we add up all the numbers, then divide by the number of numbers there are.
12+23+17+20+14+14+18+16+17+18+18= 187
187/11=17
The mean is 17.

The median is the middle number. To find this, line up all the numbers, smallest to largest.
12, 14, 14, 16, 17, 17, 18, 18, 18, 20, 23
You then cross off numbers from both sides, until you have 1 number remaining.
Your median is 17.

The mode is the number that occurs most frequently.
Your mode is 18.

3 0

3 years ago

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√24 is between which 2 numbers? Question 6 options: 1 and 2 2 and 3 3 and 4 4 and 5

Goryan [66]

The answer is: between 4 and 5

The way I figured this answer was by simply finding the square of the numbers

$1^{2} = 1$
$2^{2} =4$
$3^{2} =9$
$4^{2} =16$
$5^{2} =25$

Since 24 is between 16 and 25 then that has to be your answer.

6 0

3 years ago

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