Coordinate Geometry, Vectors and Trigonometry

Objective

A. Coordinate Geometry Students should be able to:

1. find the equation of a straight line

2. determine whether lines are parallel or mutually perpendicular using the gradients

3. find the point of intersection of two lines

4. write the equation of a circle

5. find the centre and radius of a given circle

6. find equations of tangents and normals at given points on circles

7. find the points of intersection of a curve with a straight line

B. Vectors Students should be able to:

Study Resources

2. define equal vectors

3. add and subtract vectors

4. multiply a vector by a scalar quantity

5. derive and use unit vectors

6. find displacement vectors

7. find the magnitude and direction of a vector

8. define the scalar product of two vectors:

(i) in terms of their components;

(ii) in terms of their magnitudes and the angle between them

9. find the angle between two given vectors

10. apply properties of parallel and perpendicular vectors

C. Trigonometry Students should be able to:

1. define the radian

2. convert degrees to radians and radians to degrees

3. use the formulae for arc length l = rq and sector area A = (1/2)r²q

4. evaluate sine, cosine and tangent for angles of any size given either in degrees or radians

5. evaluate the exact values of sine, cosine and tangent for q = 0, pi/6, pi/4, pi/3, pi/2, and integral multiples of each of these angles for values of q such that

6. graph the functions sin kx , cos kx , tan kx where k is 1 or 2 and

7. derive the identity cos²x + sin²x = 1

9. derive the multiple angle identities for sin 2x , cos 2x, tan 2x

10. use Specific Objectives 7, 8, and 9 above to prove simple identities

11. find solutions of simple trigonometric equations for a given range, including those involving the use of cos²q + sin²q = 1