20 a. Find the equation of the straight line joint a (0,1.5) and b(3,0)

= 2y +x =3

B . Express sintheta +2costheta in the form rsin (theta+alpha)

= root 5 sin(theta + 63.4)

c. The figure shows a map of a moor land the units of the coordinates are km and the y axis is due north. A walker leaves her car somewhere on the straight road between a and b. she walks in a straight line for a distance of 2km to a monument at the origin o. Whilst she is looking at it the fog comes down so that she cannot seethe way back to her car. She needs to work out the bearing on which she should walk.

Write down the coordinates of a point q which is 2km from o on a bearing of theta.

=(2sintheta,2costheta)

show that, for q to be on the road between a and b, theta must satisfy the equation 2sin theta + 4cos theta =3