Notice that
• <em>π</em>/2 = <em>π</em>/3 + <em>π</em>/6
• <em>π</em>/6 = <em>π</em>/3 - <em>π</em>/6
Recall the angle sum identities for sine:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
sin(<em>x</em> - <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) - cos(<em>x</em>) sin(<em>y</em>)
By adding these together, we get
sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>) = 2 sin(<em>x</em>) cos(<em>y</em>)
==> sin(<em>x</em>) cos(<em>y</em>) = 1/2 (sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>))
Now take <em>x</em> = <em>π</em>/3 and <em>y</em> = <em>π</em>/6 :
sin(<em>π</em>/3) cos(<em>π</em>/6) = 1/2 (sin(<em>π</em>/2) + sin(<em>π</em>/6))
So the blank should be filled with cos.
Answer:
1. √32
2. 4
3. 5
4. √29
5. √10
6. 5√2
Step-by-step explanation:
Use Pythagoras
Answer:
35
Step-by-step explanation:
use distributive property
5a + 5b
5×1 + 5×6
5 + 30
35
The standard deviation from the mean of the data with a variance of 36 is: B. 6.
<h3>What is Standard Deviation?</h3>
Standard deviation can be described as the average of the distance each of the value lies from the mean of the data.
The standard deviation is the square root of the variance.
Variance of the data is given already as 36.
Standard deviation = √36 = 6.
The answer is B. 6.
Learn more about the standard deviation on:
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Answer:
The two numbers are 7 and 11.
Step-by-step explanation:
x represent the first number.
y represent the second number.
x + y = 18
x - y = 4
2x = 22
x = 11
x - y = 4
(11) - y = 4
y = 7
