Due Monday, November 30.
A copy of this assignment is available as a pdf document at Lesson 44a (pdf).
NOTE added Nov 26. One of the steps in the example shown below  (sin(45π/4))  was originally left out of the discussion shown below. The discussion in the pdf document linked to above was and is correct (I hope).

Sect. 7.1:

You are asked to redo Exercise 42 in Sect. 7.1, as assigned in Lesson 44  with a slight change in the instructions, as described below. The new or changed instructions are in boldface.

Exercise 42 has instructions in the textbook. The instructions in the textbook contain identities that you are supposed to use to evaluate the quantities given. You will have to give some thought to how you use the identities to solve the problem. The basic idea is to use the given identities to reduce the quantities given to trig functions of special angles between 0 and π/2. Don't just use your calculator to evaluate the quantities given.

Step-by-step instructions for completing the problem are given below. (These are almost exactly the same as the instructions given in Lesson 44.) See also Example below.

Note on terminology: Each of the parts of Exercise 42 asks you to evaluate a trig function at a particular number, e.g.,  sin(45π/4).  This quantity (e.g.,  sin(45π/4))  will be referred to as “the value you need”; the point of the exercise is to evaluate this without using a calculator.

1. Use the identities given in the Exercise to express the given trig expression (i.e., the value you need) as a trig function of a number (angle) between  -π  and  π.  As usual, it should be clear how you are doing this.
2. If the angle obtained in step (1) above is between  0  and  π/2,  or is an integer multiple of  π/2,  just write down the answer.
3. If the angle obtained in step (1) above is bigger than  π/2  and not an integer multiple of  π/2,  USE REFERENCE ANGLES to express the value you need as a trig function of an angle between  0  and  π/2,  and then evaluate it. You will need to draw a picture to make it clear what reference angle you are using.
4. If the angle obtained in step (1) above is less than  0  and not an integer multiple of  π/2,  USE THE EVEN/ODD PROPERTIES OF THE TRIG FUNCTIONS to express the value you need as a trig function of an angle between  0  and  π,  and proceed as in Steps (2) or (3) above.

Example. Evaluate  sin(45π/4).

[NOTE: As with all examples, the point is not to remove all imagination and creativity from YOUR presentation of the solution. The point is to give you an idea of how to solve the problem and what information should be included.]

Solution.

Corrected Nov 26.
Since  45π/4 = -3π/4 + 48π/4 = -3π/4 +5(2π),
      sin(45π/4) = sin(-3π/4).   [This is step (1); you will have to THINK about what is happening here.]
Since  -3π/4  is less than  0,  we next follow step (4) and use the fact that  sin  is an odd function:
      sin(45π/4)  =  sin(-3π/4)  =  -sin(3π/4).
Since  3π/4  bigger than  π/2,  we follow step (3) and use reference angles. By drawing a picture, which is not done here, we (you) see that the reference angle for  3π/4  is  π/4, so that
            sin(3π/4) = ± sin(π/4),
where the positive value is used because the angle  3π/4  has its terminal side in the second quadrant.
So we have
      sin(45π/4) = sin(-3π/4) = -sin(3π/4) = -sin(π/4) = -1/√2.

NOTE:
These problems have instructions in the textbook.
These problems have instructions given above.
You are expected to note the instructions.
You are expected to read the instructions.
You are expected to follow the instructions.
You will lose points -- perhaps a substantial number of points -- if you do not read and follow the instructions.