sin(<em>θ</em>) + cos(<em>θ</em>) = 1
Divide both sides by √2:
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = 1/√2
We do this because sin(<em>x</em>) = cos(<em>x</em>) = 1/√2 for <em>x</em> = <em>π</em>/4, and this lets us condense the left side using either of the following angle sum identities:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
cos(<em>x</em> - <em>y</em>) = cos(<em>x</em>) cos(<em>y</em>) - sin(<em>x</em>) sin(<em>y</em>)
Depending on which identity you choose, we get either
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = sin(<em>θ</em> + <em>π</em>/4)
or
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = cos(<em>θ</em> - <em>π</em>/4)
Let's stick with the first equation, so that
sin(<em>θ</em> + <em>π</em>/4) = 1/√2
<em>θ</em> + <em>π</em>/4 = <em>π</em>/4 + 2<em>nπ</em> <u>or</u> <em>θ</em> + <em>π</em>/4 = 3<em>π</em>/4 + 2<em>nπ</em>
(where <em>n</em> is any integer)
<em>θ</em> = 2<em>nπ</em> <u>or</u> <em>θ</em> = <em>π</em>/2 + 2<em>nπ</em>
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We get only one solution from the second solution set in the interval 0 < <em>θ</em> < 2<em>π</em> when <em>n</em> = 0, which gives <em>θ</em> = <em>π</em>/2.
Answer: 40:80:80
Step-by-step explanation:
The ratio is 1:2:2. This means, for every 5, the money is split in a ratio of 1:2:2. Let’s calculate how many 5s there are in 200. 200 / 5 = 40. So, the money will be split in 1:2:2 every 5 dollars 40 times.
Excellent. So, we can easily find out the ratio by multiplying the ratio 1:2:2 by 40. 1*40:2*40:2*40 = 40:80:80. Let’s add these up, and see if they result in 200. 40 + 80 + 80 = 200. So, our answer is correct.
Hope this helps!
1/2 m-3/4 * 8=16
1/2 m- 3*2=16
1/2 m-6=16
1/2 m =22
m=44
Answer:
we have to put the numbers in order..
(121,122,125, 126,132),M,(135,136,136,138,140)
Step-by-step explanation:
minimum : (smallest number) = 121
Q1 : 125
Q2 (median) : (132 + 135) / 2 = 267/2 = 133.5
Q3 : 136
maximum : (largest number) = 140
I did this a long time ago so im not so sure
Answer:
A.) 10 years old
Step-by-step explanation:
Sam: John - 14
S = J - 14
S x J = 240
10 = J - 14
0 = J - 14 - 10
-J = -24
J = 24
10 x 24 = 240
