1. ## trigonometry Addition Formulae (v)

The diagram shows a kite whose leading diagonal forms the diameter of a circle. Find the exact value of sin XOY

What I want to know is, do I need to find the diameter, if so, how?

2. Originally Posted by r_maths

The diagram shows a kite whose leading diagonal forms the diameter of a circle. Find the exact value of sin XOY

What I want to know is, do I need to find the diameter, if so, how?
That means the inscribed angle X0Y is 90 degree.
Thus, sin 90 = 1

3. Originally Posted by ThePerfectHacker
That means the inscribed angle X0Y is 90 degree.
Thus, sin 90 = 1
my bad, the sides are not equal so you cant 360/4.
root 5 & 3 are the length of the sides of the kite

the answer is 3 root5 / 7
i dont know how to arrive at that.
(just to let you know, no calculator allowed)

4. Hello, r_maths!

The diagram shows a kite whose leading diagonal forms the diameter of a circle.
Find the exact value of $\sin(XOY)$.

Look at half of the kite . . .
Code:
      Z
*
| *   _
|   *√5
|     *
__ |   90° * Y
√14 |      *
|     *
|    *
|   * 3
|θ *
| *
|*
*
O

Since $ZO$ is a diameter, $\angle Y = 90^o.$

Using Pythagorus, we find that: . $ZO = \sqrt{14}$

Let $\theta = \angle ZOY$
Then: . $\sin\theta = \frac{\sqrt{5}}{\sqrt{14}},\;\cos\theta = \frac{3}{\sqrt{14}}$

Then: . $\sin(XOY) \:=\:\sin(2\theta) \:=\:2\sin\theta\cos\theta \:=\:2\left(\frac{\sqrt{5}}{\sqrt{14}}\right)\left (\frac{3}{\sqrt{14}}\right) \:=\:\frac{3\sqrt{5}}{7}$

5. Originally Posted by Soroban
Hello, r_maths!

Look at half of the kite . . .
Code:
      Z
*
| *   _
|   *√5
|     *
__ |   90° * Y
√14 |      *
|     *
|    *
|   * 3
|θ *
| *
|*
*
O

Since $ZO$ is a diameter, $\angle Y = 90^o.$
how did you work out that angle was 90 ?