有幾條數唔識計.10點~~~~~

1) 6 : x : y = 4 : 5 : 6 (intercept theorem)

First, 6 : x = 4 : 5
x = 6 / (4 / 5) = 7.5

Then 6 : y = 4 : 6
y = 6 / (4 / 6) = 9

2)The range of θ cannot be shown properly. I guess it is 0 <= θ <= 90.

tanθ cosθ = 0
tanθ = 0 or cosθ = 0
θ = 0 or θ = 90 (rejected)

We have to reject θ = 90 because tan 90 is undefined.

So θ = 0 only.

In fact, it is much faster if you calculate like below:

tanθ cosθ = 0
(sinθ / cosθ) cosθ = 0
sinθ = 0
θ = 0

3)
If you are F.3:
Construct a right-angled triangle.
Let x be the adjacent side, y be the opposite side and r be the hypotenuse of θ. Then,

sinθ = y/r and cosθ = x/r

Within 0 and 45, the adjacent side is longer than the opposite side, i.e. x > y.

Hence, cosθ > sinθ for 0 <= θ < 45