https://file.aiquickdraw.com/mathbot/file/1729049692577ush9szy9.jpg

The image depicts a right-angled triangle with one of the angles being \( 45^\circ \), and it asks to determine \(\tan 45^\circ\), \(\sin 45^\circ\), and \(\cos 45^\circ\).

For a right-angled triangle with a \( 45^\circ \) angle, we can use the following standard trigonometric ratios:

1. **\(\tan 45^\circ\)**:
   \[
   \tan \theta = \frac{\text{opposite}}{\text{adjacent}}
   \]
   For \( \theta = 45^\circ \), the opposite and adjacent sides are equal, so:
   \[
   \tan 45^\circ = 1
   \]

2. **\(\sin 45^\circ\)**:
   \[
   \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}
   \]
   Using the standard right triangle for \(45^\circ\), where the opposite and adjacent sides are the same and the hypotenuse is \( \sqrt{2} \) times the side:
   \[
   \sin 45^\circ = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}
   \]

3. **\(\cos 45^\circ\)**:
   \[
   \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}
   \]
   Similarly:
   \[
   \cos 45^\circ = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}
   \]

In summary:
- \(\tan 45^\circ = 1\)
- \(\sin 45^\circ = \frac{\sqrt{2}}{2}\)
- \(\cos 45^\circ = \frac{\sqrt{2}}{2}\)

Would you like further details or have any questions?

Here are 5 related questions:
1. How do we determine the length of the hypotenuse in a right triangle using sine or cosine?
2. Can you explain why \(\tan 45^\circ = 1\) geometrically?
3. How can we calculate other trigonometric values for angles like \(30^\circ\) or \(60^\circ\)?
4. What is the relationship between sine and cosine for complementary angles?
5. How do we use these trigonometric ratios in real-world applications?

**Tip**: Memorizing the sine and cosine values for common angles like \(30^\circ\), \(45^\circ\), and \(60^\circ\) can help in quickly solving trigonometric problems.

Tentukan Tan 45°, Sin 45°, Cos 45° pada segitiga dengan sudut 45°.

Pelajari cara menentukan nilai Tan 45°, Sin 45°, dan Cos 45° pada segitiga siku-siku dengan sudut 45°. Temukan rumus trigonometri yang relevan untuk memecahkan masalah ini. Cocok untuk siswa kelas 9-11.

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