Cos Function

### Program Information

Name: Cos Function
Domain: Numerical Program
Functionality: Cos function in math
Input: $x$: A certain Real Number
Output: $y$: The value of $\cos x$

#### Reference

 Automated Test Data Generation on the Analyses of Feature Models:A Metamorphic Testing Approach
https://doi.org/10.1109/ICST.2010.20;
Testing Embedded Software by Metamorphic Testing: a Wireless Metering System Case Study
https://doi.org/10.1109/LCN.2011.6115306;
Verification of Compartmental Epidemiological Models using Metamorphic Testing, Model Checking and Visual Analytics
https://doi.org/10.1109/BioMedCom.2012.18;
Search-Based Inference of Polynomial Metamorphic Relations https://doi.org/10.1145/2642937.2642994; 

### MR Information

#### MR1------

Description:
Property: $\cos x=\cos(-x)$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x$
Follow-up output: $\cos (-x)$
Input relation: $x \Rightarrow (-x)$
Output relation: $\cos x=\cos(-x)$
Pattern:

#### MR2------

Description:
Property: $\cos x=\cos(x+2\pi)$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x+2\pi$
Follow-up output: $\cos (x+2\pi)$
Input relation: $x \Rightarrow (x+2\pi)$
Output relation: $\cos x=\cos(x+2\pi)$
Pattern:

#### MR3------

Description:
Property: $\cos (2x)=2\cos(x)^2 - 1$
Source input: $x$
Source output: $\cos x$
Follow-up input: $2x$
Follow-up output: $\cos (2x)$
Input relation: $x \Rightarrow (2x)$
Output relation: $\cos (2x)=2\cos(x)^2 - 1$
Pattern:

#### MR4------

Description:
Property: $\cos(x)+\cos(-x-\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x-\pi$
Follow-up output: $\cos (-x-\pi)$
Input relation: $x \Rightarrow (-x-\pi)$
Output relation: $\cos(x)+\cos(-x-\pi)=0$
Pattern:

#### MR5------

Description:
Property: $\cos(x)-\cos(x-2\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x-2\pi$
Follow-up output: $\cos (x-2\pi)$
Input relation: $x \Rightarrow (x-2\pi)$
Output relation: $\cos(x)-\cos(x-2\pi)=0$
Pattern:

#### MR6------

Description:
Property: $\cos(x)+\cos(x-\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x-\pi$
Follow-up output: $\cos (x-\pi)$
Input relation: $x \Rightarrow (x-\pi)$
Output relation: $\cos(x)+\cos(x-\pi)=0$
Pattern:

#### MR7------

Description:
Property: $\cos(x)-\cos(-x-3\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x-3\pi$
Follow-up output: $\cos (-x-3\pi)$
Input relation: $x \Rightarrow (-x-3\pi)$
Output relation: $\cos(x)-\cos(-x-3\pi)=0$
Pattern:

#### MR8------

Description:
Property: $\cos(x)-\cos(-x+2\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x+2\pi$
Follow-up output: $\cos (-x+2\pi)$
Input relation: $x \Rightarrow (-x+2\pi)$
Output relation: $\cos(x)-\cos(-x+2\pi)=0$
Pattern:

#### MR9------

Description:
Property: $\cos(x)+\cos(x+\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x+\pi$
Follow-up output: $\cos (x+\pi)$
Input relation: $x \Rightarrow (x+\pi)$
Output relation: $\cos(x)+\cos(x+\pi)=0$
Pattern:

#### MR10------

Description:
Property: $\cos^2(x)+\cos^2(-x-0.5\pi)-1=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x-0.5\pi$
Follow-up output: $\cos (-x-0.5\pi)$
Input relation: $x \Rightarrow (-x-0.5\pi)$
Output relation: $\cos^2(x)+\cos^2(-x-0.5\pi)-1=0$
Pattern:

#### MR11------

Description:
Property: $\cos^2(-0.5x-1.5\pi)+0.5\cos(x)-0.5=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-0.5x-1.5\pi$
Follow-up output: $\cos (-0.5x-1.5\pi)$
Input relation: $x \Rightarrow (-0.5x-1.5\pi)$
Output relation: $\cos^2(-0.5x-1.5\pi)+0.5\cos(x)-0.5=0$
Pattern:

#### MR12------

Description:
Property: $\cos^2(x)-\cos^2(x+\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x+\pi$
Follow-up output: $\cos (x+\pi)$
Input relation: $x \Rightarrow (x+\pi)$
Output relation: $\cos^2(x)-\cos^2(x+\pi)=0$
Pattern:

#### MR13------

Description:
Property: $\cos^2(x)+\cos^2(-x)-2\cos(x)\cos(-x)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x$
Follow-up output: $\cos (-x)$
Input relation: $x \Rightarrow (-x)$
Output relation: $\cos^2(x)+\cos^2(-x)-2\cos(x)\cos(-x)=0$
Pattern:

#### MR14------

Description:
Property: $\cos^2(0.5x-2\pi)-0.5\cos(x)-0.5=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $0.5x-2\pi$
Follow-up output: $\cos (0.5x-2\pi)$
Input relation: $x \Rightarrow (0.5x-2\pi)$
Output relation: $\cos^2(0.5x-2\pi)-0.5\cos(x)-0.5=0$
Pattern:

#### MR15------

Description:
Property: $\cos^2(x)+\cos(x)\cos(-x+\pi)-\cos(x)-\cos(-x+\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x+\pi$
Follow-up output: $\cos (-x+\pi)$
Input relation: $x \Rightarrow (-x+\pi)$
Output relation: $\cos^2(x)+\cos(x)\cos(-x+\pi)-\cos(x)-\cos(-x+\pi)=0$
Pattern:

#### MR16------

Description:
Property: $\cos^2(x)-\cos(x)\cos(-x)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x$
Follow-up output: $\cos (-x)$
Input relation: $x \Rightarrow (-x)$
Output relation: $\cos^2(x)-\cos(x)\cos(-x)=0$
Pattern:

#### MR17------

Description:
Property: $\cos^2(x)+0.5\cos^2(x+\pi)+1.5\cos(x)\cos(x+\pi)-1.5\cos(x)-1.5\cos(x+\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x+\pi$
Follow-up output: $\cos (x+\pi)$
Input relation: $x \Rightarrow (x+\pi)$
Output relation: $\cos^2(x)+0.5\cos^2(x+\pi)+1.5\cos(x)\cos(x+\pi)-1.5\cos(x)-1.5\cos(x+\pi)=0$
Pattern:

#### MR18------

Description:
Property: $\cos^2(x)-\cos(x)\cos(-x+2\pi)-\cos(x)+\cos(-x+2\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $-x+2\pi$
Follow-up output: $\cos (-x+2\pi)$
Input relation: $x \Rightarrow (-x+2\pi)$
Output relation: $\cos^2(x)-\cos(x)\cos(-x+2\pi)-\cos(x)+\cos(-x+2\pi)=0$
Pattern:

#### MR19------

Description:
Property: $\cos^2(0.5x)-0.5cos(x)-0.5=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $0.5x$
Follow-up output: $\cos (0.5x)$
Input relation: $x \Rightarrow (0.5x)$
Output relation: $\cos^2(0.5x)-0.5cos(x)-0.5=0$
Pattern:

#### MR20------

Description:
Property: $\cos^2(x)+\cos^2(x-2\pi)-2\cos(x)\cos(x-2\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x-2\pi$
Follow-up output: $\cos (x-2\pi)$
Input relation: $x \Rightarrow (x-2\pi)$
Output relation: $\cos^2(x)+\cos^2(x-2\pi)-2\cos(x)\cos(x-2\pi)=0$
Pattern:

#### MR21------

Description:
Property: $\cos^2(x)+3\cos^2(x-\pi)+4\cos(x)\cos(x-\pi)=0$
Source input: $x$
Source output: $\cos x$
Follow-up input: $x-\pi$
Follow-up output: $\cos (x-\pi)$
Input relation: $x \Rightarrow (x-\pi)$
Output relation: $\cos^2(x)+3\cos^2(x-\pi)+4\cos(x)\cos(x-\pi)=0$
Pattern:
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