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11 Graph each of these functions on a separate set of axes Label your graph (a) f (x) = x 2 3x x+1 (b) g (x) = 2x (c) h(x) = x 2 x (d) f (x) = 2x + 1 (e) g (x) = x 2 + x (f) h(x) = x + 5 12 Calculate each of the following trigonometric quantities (a) sin(2 /3) (b) tan( /6) (c) sec(3 /4) (d) csc(5 /4) (e) cot( 11 /4) (f) cos( /4) 13 Calculate the left and right sides of the twelve fundamental trigonometric identities for the values = /6 and = /3, thus confirming the identities for these particular values 14 Sketch the graphs of each of the following trigonometric functions (a) f (x) = cos 2x (b) g (x) = sin(x /2) (c) h(x) = cot(x + ) (d) f (x) = tan(x + ) (e) g (x) = cos(x/6) (f) h(x) = cos( + [x/2]) 15 Convert each of the following angles from radian measure to degree measure (a) = /12 (b) = /2 (c) = 27 /4 (d) = 3 /16 (e) = 4 (f) = 7 16 Convert each of the following angles from degree measure to radian measure (a) = 45 (b) = 20

3 Capitalize the rst, last, and all important words in a title (Use italics to indicate a book, play, or movie title; place article titles within quotation marks)

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As just explained, value types, such as int or char, are passed by value to a method This means that changes to the parameter that receives a value type will not affect the actual argument used in the call You can, however, alter this behavior Through the use of the ref and out keywords, it is possible to pass any of the value types by reference Doing so allows a method to alter the argument used in the call Before going into the mechanics of using ref and out, it is useful to understand why you might want to pass a value type by reference In general, there are two reasons: to allow a method to alter the contents of its arguments or to allow a method to return more than one value Let s look at each reason in detail Often you will want a method to be able to operate on the actual arguments that are passed to it The quintessential example of this is a Swap( ) method that exchanges the values of its two arguments Since value types are passed by value, it is not possible to write a method that swaps the value of two ints, for example, using C# s default call-by-value parameter passing mechanism The ref modifier solves this problem As you know, a return statement enables a method to return a value to its caller However, a method can return only one value each time it is called What if you need to return two or more pieces of information For example, what if you want to create a method that decomposes a floating-point number into its integer and fractional parts To do this requires that two pieces of information be returned: the integer portion and the fractional component This method cannot be written using only a single return value The out modifier solves this problem.

8:

(c) (d) (e) (f)

The ref parameter modifier causes C# to create a call-by-reference, rather than a call-byvalue The ref modifier is specified when the method is declared and when it is called Let s begin with a simple example The following program creates a method called Sqr( ) that returns in-place the square of its integer argument Notice the use and placement of ref

// Use ref to pass a value type by reference using System; class RefTest { // This method changes its argument Notice the use of ref public void Sqr(ref int i) { i = i * i; } } class RefDemo { static void Main() { RefTest ob = new RefTest(); int a = 10; ConsoleWriteLine("a before call: " + a); obSqr(ref a); // notice the use of ref ConsoleWriteLine("a after call: " + a); } }