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Trigonometry means measurement of triangles. Consider its parts: tri means three, gon means angle, and metry means measure. Thus, in trigonometry we study the measurement of triangles. The following ratios relate the sides and acute angles of a right triangle: 1. Tangent ratio: The tangent (abbreviated tan ) of an acute angle equals the length of the leg opposite the angle divided by the length of the leg adjacent to the angle. 2. Sine ratio: The sine (abbreviated sin ) of an acute angle equals the length of the leg opposite the angle divided by the length of the hypotenuse. 3. Cosine ratio: The cosine (abbreviated cos ) of an acute angle equals the length of the leg adjacent to the angle divided by the length of the hypotenuse. Thus in right triangle ABC of Fig. 8-1,

The String class implemented in this chapter would be inefficient for writing a text file or for any purpose that involved many instances of the same word (like I the " or I New York I ). This inefficiency can be reduced significantly by allowing many objects to share the same buf space in memory. However, using several pointers to point to the same data can cause problems. (See Questions Example 10.1 and Example 10.2.) These potential problems can be overcome by making the initial byte in buf a counter that keeps track of how many objects are using that buffer. For example, the declarations

Fig. 8-1

String sl("France"), s2("Spain"), s3("France"), s4("France");

Our goal will be to transform the appearance of these forms into the forms shown in Figs. 7.19(a) and (b).

length of leg opposite A length of leg adjacent to A length of leg opposite A length of hypotenuse length of leg adjacent to A length of hypotenuse a c

would be represented as:

memory:

length of leg opposite B length of leg adjacent to B length of leg opposite B length of hypotenuse length of leg adjacent to B length of hypotenuse b c

Note that each string occupies len + 2 bytes in memory. Also note that the initial byte is storing an nonnegative integer as a char, so it must remain in the range 0 to 127. Modify the String implementation in this chapter to represent strings this way. The main changes have to be made to the constructors, the destructor, and the assignment operator.

If A and B are the acute angles of a right triangle, then sin A cos B cos A sin B tan A 1 tan B tan B 1 tan A

switch is off, comparisons are made without regard to case, so that I NeXT lt and I next " would be regarded as equal strings. One way to implement this feature is to add the s tat i c data member

A scientific calculator can compute the sine, cosine, and tangent of an angle with the SIN, COS, and TAN buttons, respectively. Make sure the calculator is set to degrees (DEG). For those without a calculator, a table of sines, cosines, and tangents is in the back of this book.

static int sensitivity;

Using the table of sines, cosines, and tangents The following values were taken from a table of sines, cosines, and tangents. State, in equation form, what the values on the first three lines mean. Then use the table at the back of this book to complete the last line.

static int setSensitivity();

Fig. 7.19(a)

10.1 If the second constructor had default values for both of its arguments, then a declaration like this

(a) (b) (c) (d)

String s; would be ambiguous. Any constructor which has default values for all of its arguments is a default constructor, and a class may have only one default constructor. 10.2 The copy constructor that is automatically provided by the compiler merely duplicates the member data. This would result in different objects having their own (different) buf pointers, but they would point to the same C-string. That could be disastrous, for example, if one were changed or deleted. 10.3 See the answer to Question 10.2. 10.4 Our string class is more efficient when making comparisons. It is less efficient with its overloaded stream extraction operator >> which uses a 256-byte buffer. It would also be inefficient in a textprocessing environment because of the overhead of its constructors. (See Problem 10.3 1.)

(a) sin 1 (b) sin 30 (c) sin 60 0.0175; cos 1 0.5000; cos 30 0.8660; cos 60 0.9998; tan 1 0.8660; tan 30 0.5000; tan 60 0.0175 0.5774 1.7321

11

(d) In the table of trigonometric functions, the cosine value 0.3420 is on the 70 line; hence, the angle measures 70 . Then, from the table, sin 70 0.9397 and tan 70 2.7475.