Course Revision Set2

1. The line y – x = -10 cuts the circle x² + y² + 4x + 6y –40 = 0 at the points A and B. Find the coordinates of A and B and find the length AB.

2. Show that the triangle with vertices A(5, 7, -5), B(4, 7, -3) and C(2, 7, -4) is isosceles and right angled by:

a) the converse of Pythagoras

b) the scalar product

3. If sinA = 4/5 and tanB = 5/12 show that the exact value of sin(A + B) = 63/65 and

tan(A – B) =33/56

4.

ABCD is a square side 10cm. EB is xcm and CF is 2xcm.

Show that the area of triangle DEF is given by:

Area DEF = 50 - 10x + x²

Find the value of x which minimises DEF and find this minimum area.

5. Solve for 0 < x < 360⁰

a) 2cos²(x) =

b) sin(2x) = 2cos²(x)