Problem Solving with Nested Loop
Problem Set
The following problem sets are intended for practice.
Attempt these on your own.
??? example "Sin x"
## Sin x
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18 | Approximate $\text{sin}(x)$ using Taylor series with $k$ iterations.
### Task
Write Python code to compute and print the approximate of $\text{sin}$ of `#!py3 x` with `#!py3 k` number of iterations.
### Assumptions
- `#!py3 x` is a non-negative floating point between 0 and $2\pi$ (_i.e.,_ `#!py3 0 <= x < 6.28...`).
- `#!py3 n` is a non-negative integer (_i.e.,_ `#!py3 n >= 0`).
- `#!py3 x` and `#!py3 n` are initialized.
### Restrictions
- You cannot use the built-in `#!py3 sin` function from the `#!py3 math` module.
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??? example "Cos x"
## Cos x
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18 | Approximate $\text{cos}(x)$ using Taylor series with $k$ iterations.
### Task
Write Python code to compute and print the approximate of $\text{cos}$ of `#!py3 x` with `#!py3 k` number of iterations.
### Assumptions
- `#!py3 x` is a non-negative floating point between 0 and $2\pi$ (_i.e.,_ `#!py3 0 <= x < 6.28...`).
- `#!py3 n` is a non-negative integer (_i.e.,_ `#!py3 n >= 0`).
- `#!py3 x` and `#!py3 n` are initialized.
### Restrictions
- You cannot use the built-in `#!py3 cos` function from the `#!py3 math` module.
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??? example "Next Prime"
## Next Prime
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12 | Given an integer $n$, we want to find the number $m$ such that $m \geq n$ and $m$ is a prime number.
### Task
Write Python code to compute and print the first prime number that is larger than or equal to the input `#!py3 n`.
### Assumptions
- `#!py3 n` is a non-negative integer (_i.e.,_ `#!py3 n >= 0`).
- `#!py3 x` is initialized.
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