Calculating an approximation of sin^2⁡〖(x)〗+ cos^2⁡〖(x)〗 and determining how accurate it is.

[AhabsWhiteWhale]

What is wrong with my calculations of sinx & cosx? The formula to calculate the two was given and I believe I have written the code correctly, however when the program runs, it simply displays the value entered in. (exp.) I enter in 5, program runs, displays 5 as my sinx. What have I done wrong here?

These are the equations we were told to use

sin⁡(x)= x- 1/6 x^3+ 1/120 x^5

cos⁡(x)= 1- 1/2 x^2+1/24 x^4

// 
// Take Home Test #1
// 9-27-13

// Library includes
#include <stdio.h>
#include <math.h>

//Main entry point
int main(void){

	//Variable declaration
	float valuex = 0.0;
	float sinx   = 0.0;
	float cosx   = 0.0;

	//Displaying a message to the user
	printf("Approximation of sin^2(x)+cos^2(x):\n");

	//Read in a float value from the user
	printf("Please enter a value between 0 and 5: ");
	scanf("%f", &valuex);

	//Making sure the value is within defined range
	if (valuex >= 0 && valuex <= 5 ){
		sinx = valuex - 1/6*(valuex*valuex*valuex) + 1/120*(valuex*valuex*valuex*valuex*valuex); 
	printf("sin(x) = %f.\n", sinx);
		cosx = 1 - 1/2*(valuex*valuex) + 1/24*(valuex*valuex*valuex*valuex);
	printf("cos(x) = %f.\n", cosx);
	}	else if (valuex < 0 ){
		printf("Please enter a valid value.\n");
	}	else if (valuex > 5 ){
		printf("Please enter a valid value.\n");
	}

	//Calculating and displaying the approximation of sin^2(x)+cos^2(x)
	//sinx = valuex - 1/6*(valuex*valuex*valuex) + 1/120*(valuex*valuex*valuex*valuex*valuex); 
	//printf("sin(x) = %f.\n", sinx);
	//cosx = 1 - 1/2*(valuex*valuex) + 1/24*(valuex*valuex*valuex*valuex);
	//printf("cos(x) = %f.\n", cosx);
	
	//valuex - 1/6*(valuex*valuex*valuex) + 1/120*(valuex*valuex*valuex*valuex*valuex) 

}

[Chervil]

I think you are running into an integer divide problem.
If we treat the numbers as integers, 1/6 == 0 and 1/120 == 0

The solution is to make at least one of the values in the divide operation a floating-point type:

	sinx = valuex - 1.0f/6*(valuex*valuex*valuex) + 1.0f/120*   (valuex*valuex*valuex*valuex*valuex);
	cosx = 1 - 1.0f/2*(valuex*valuex) + 1.0f/24*(valuex*valuex*valuex*valuex);

[AhabsWhiteWhale]

This worked! Thanks you so much! Would you mind explaining my mistake more thoroughly? Why does simply placing 1/6 or 1/24 as a fractional multiplier not work?

[Chervil]

You should try a simple code example for yourself, to see how integer division works.

There are two important things, anything after the decimal point is discarded, so that 22/7 gives exactly 3 rather than 3.14285 and 1/2 gives exactly 0 instead of 0.5

The other point is that any literals such as 22 or 3.14 are considered by the compiler to be of a particular type such as int, float, double and so on. If there is no decimal point, the value is an integer. With a decimal point, such as 22.0 or 1.0, the value is of type double
You can further specify the type with a subscript letter such as f for float. (note that floats are less precise than doubles)

For more information see the tutorial page: http://www.cplusplus.com/doc/tutorial/constants/