MAT question help

- How did they know that the middle sector of A was at a degree of 90 even though it can be seen from the diagram that isnt always correct..
- I dont understand how they've worked out the area of the triangle and the placement of theta also confuses me

If anyone wants to help me by solving it you're most welcome

Question 4 part (ii) in case anyone else want to look.

Angle subtended by middle sector is 90 because, angle to the left is theta, and angle to the right is 90 - theta, and since the total is 180, the remainder - the sector's angle - is 90.

Since the radius of the circle is "1", then the x co-ordinates of -cos theta and sin theta, imples the angles marked are theta.
Triangles are congruent, having two sides next to the right angle of cos theta and sin theta, hence the area formula used. (1/2) base times height, and times 2 as there are two identical triangles.

How is angle to the left theta and angle to the right 90-theta.

I also dont get the co-ordinates bit like how can you put -cos and sin on the same x axis

For the left.
Since the x-coordinate is -cos theta, and the semicicle has radius 1, then that's the value you'd get if the angle to the left was theta. Hence the angle is theta. No other value in the range 0 to 90 will do.

For the right.
Similar argument for the angle theta, and hence the angle at the origin is 90-theta.



I don't see your problem really. You're given the two coordinates, and they happen to be function of theta. Their actual position is going to depend on what theta is. We can't say, for example, that one is between 0.4 and 0.5, only that it is somewhere between 0 and 1.