V. INVERSE TRIGONOMETRIC FUNCTIONS

1. (i) Sketch the graph of . State the domain and range. Does y has a minimum value ? If so, is this a stationary value on the curve ?

(ii) For what values of x is defined ? Sketch the graph of y = , stating its range.

(iii) Define the function y = , and sketch it. Does y has a maximum value ? Explain your answer from the sketch.

2. Without using calculator, find the value of:

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

3. Find the exact value of

(a) (b)

(c) (d)

4. Evaluate without tables:

(a) (b) (c)

(d) (e) (f)

5. Without tables, find the value of:

(a) (b) (c)

(d) (e) (f)

6. (i) Write down the result of sin(A + B) and hence deduce the result for . Use this to evaluate .

(ii) Write down a result for cos(x + y) and show that . Hence deduce the exact value of

7. Determine the domain and range of each of the following functions:

(a) (b) (c)

8. State the domain and range each of the following functions:

(a) (b) (c)

9. (i) Find the maximum value of the function 2x(1 - x) and hence determine the range of for 0 < x < 1.

(ii) Find the least value of x(x - 2) and hence determine the range of :

(a) (b) if for 0 < x < 2.

10. State the domain and range of cosx . Hence determine the domain and range of each of the following functions:

(a) (b) (c)

(d) (e) (f)

11. If n is a positive integer, determine the limits of the following sequences when:

(a) (b) (c)

(d) (e) (f)

12. Determine whether each of the following functions is an even or odd:

(a) y = sinx (b) (c)

(d) (e) (f)

(g) (h) (i)

13. (i) Prove that is an odd function.

(ii) Provided -1 < x < 1 show that = x .

(iii) Hence, draw the graph of y = .

(iv) Using a similar method to show that

(a) for -1 < x < 1 (b) for all x.