Write a C program with a separate function which calculates the sine function from the first principles according to the formula below. The error in your function should be less than 1×10-6 which determines the minimum number of terms to be included in the calculation. Compare the result with the standard sin() library function. See image.

Write a C program that calculates the speed of sound (a) in air at a given temperature T (Farenheit) using the formula below and output to a text file, in the form of a table, the speed of sound at each temperature in (Celsius) over 0 to 100 Celsius range. See image.

Design and implement a class Quadratic to represent a quadratic function, a function of the form. See image.

The class should have the following features:

- Include private data members for coefficients a, b, and c.
- Define a default constructor and a constructor that initializes a, b, and c to the values of its three parameters.
- Overload the input extraction operator to input a Quadratic object as three coefficients.
- Overload the output insertion operator to display the quadratic in this form: 5x^2 + 6x + 17.
- Define a member function to evaluate the function at a value for x provided as a parameter, returning the value calculated as the function result.
- Define a member function that displays the two real roots of the quadratic or an appropriate message if the function has a double root or no real roots. You need to use the quadratic formula in this function: See image.

Write a program to test your class.

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