COMP101 EXAMPLE PROBLEM - SINE, COSINE AND TANGENT

Specimen Answer

1. REQUIREMENTS

Produce a Java class that will return the sine, cosine and tangent of a given angle between 0.0 and 90.0 degrees (Figure 1).

Figure 1: Sine, cosine and tangent trigonometric identities

2. ANALYSIS AND DESIGN

The design comprises a single class, TrigIdentitiesApp; all other methods used are contained in existing classes that come with the Java API.

2.1 `TrigIdentitiesApp` Class

A Nassi-Shneiderman presented in Figure 2.

NASSI-SHNEIDERMAN CHART FOR TRIG IDENTITIES APP METHOD

Fig 2: Nassi-Shneidermancharts for TrigIdentitiesApp class method

Field Summary
`private static Scanner`	`keyboardInput` A class instance to facilitate input from the keyboard.
`private static final double`	`DEC_2_RAD` A class constant facilitate conversion from degrees to radians.

Method Summary
`public static void`	`main(String[] args)` Allows user to input an angle (in degrees) which is then converted to radians and the appropriate values tangent, sine and cosine ratios produced.

3. IMPLEMENTATION

// TRIGONOMETRIC IDENTITIES
// Frans Coenen
// Tuesday 12 March 1999
// Modified: Saturday 17 September 2005 (Java 2.5)
// The University of Liverpool, UK   

import java.util.*;

class TrigIdentitiesApp {

    // ------------------- FIELDS ------------------------ 
        
    // Create BufferedReader class instance

    static Scanner keyboardInput = new Scanner(System.in);
		
    // Constants
    
    private static final double DEG_2_RAD = Math.PI/180.0;
    
    // ------------------ METHODS ------------------------  
    
    public static void main(String[] args) {
    	double angle;
	
    	// Input an angle    
    	System.out.print("Input an anagle between 0 and 90 " +
				        "degrees inclusive: ");
    	angle = keyboardInput.nextDouble();
	
	// Convert to radians	
	angle = angle*DEG_2_RAD;
	
	// Sine Angle	
	System.out.println("Sine is:    " + Math.sin(angle));
	
	// Cosine Angle	
	System.out.println("Cosine is:  " + Math.cos(angle));
	
	// Tangent Angle	
	System.out.println("Tangent is: " + Math.tan(angle));
	}
    }

Table 1: Trigonometric identities program

Note that the implementation given in Table 1 uses the constant, DEG_2_RAD, to convert input in degrees to radians.

4. TESTING

TEST CASE	EXPECTED RESULT
RADIUS
`e`	`java.lang.NumberFormatException`
`10.e`	`java.lang.NumberFormatException`

Arithmetic testing: We have one input therefore we should test negative, zero and positive inputs. A suitable set of test cases is given in the table to the right. Note that we have include a number of positive values (30, 45, 60 and 90) because these have well known results.

angle	Sine	Cosine	Tangent
TEST CASE		EXPECTED RESULT
`-90`	`-1.00000`	`6.12303`	`-1.63318`
`0`	`0.00000`	`1.00000`	`0.00000`
`30`	`0.50000`	`0.86602`	`0.57735`
`45`	`0.70711`	`0.70711`	`1.00000`
`60`	`0.86602`	`0.50000`	`1.73205`
`90`	`1.00000`	`6.12303`	`1.63318`

An alternative implementation is given in Table 2 where the toRadians class methhod from the Math is used.

// TRIGONOMETRIC IDENTITIES VERSION 2
// Frans Coenen
// Tuesday 12 March 1999
// Modified: Saturday 17 September 2005 (Java 2.5)
// The University of Liverpool, UK   

import java.util.*;

class TrigIdentitiesVer2App {

    // ------------------- FIELDS ------------------------ 
        
    // Create BufferedReader class instance
    static Scanner keyboardInput = new Scanner(System.in);
		
    // Constants    
    private static final double DEG_2_RAD = Math.PI/180.0;
    
    // ------------------ METHODS ------------------------  
    
    public static void main(String[] args) {
    	double angle;
	
    	// Input an angle    
    	System.out.print("Input an anagle between 0 and 90 " +
				      "degrees inclusive: ");
    	angle = keyboardInput.nextDouble();
	
	// Convert to radians	
	angle = Math.toRadians(angle);
	
	// Sine Angle	
	System.out.println("Sine is:    " + Math.sin(angle));
	
	// Cosine Angle	
	System.out.println("Cosine is:  " + Math.cos(angle));
	
	// Tangent Angle	
	System.out.println("Tangent is: " + Math.tan(angle));
	}
    }

Table 2: Alternative trigonometric identities program

Created and maintained by Frans Coenen. Last updated 17 September 2005