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:
$220.18
Step-by-step explanation:
The amount A(n) accrued for P dollars saved at r% annual interest for a period of n years compounded k times is derived using the formula:
In Jayden's case:
- A(n)=$400
- r=12%=0.12
- n=5 years
- k=12 Months
We want to determine the amount Jayden put in the savings account.
Jayden earned $220.18 from doing odd jobs.
The domain: {-4; -1; 0; 2; 4}
The range: {-2; 0; 1; 3}
Yes. The relation is a function.
9514 1404 393
Answer:
1/3
Step-by-step explanation:
If the ratio is common, you can choose any successive numbers to compute it. Smaller numbers may be more familiar. The ratio is ...
5/15 = 1/3
Answer:
what I'm bored
Step-by-step explanation:
what's u need help with anything I'
