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The diagram shows a right triangle in standard position with angle \(\theta\), and you are tasked to find \(\sin \theta\), \(\cos \theta\), and \(\tan \theta\). Based on the graph:

- The triangle's opposite side (vertical) rises from 0 to 6 units.
- The adjacent side (horizontal) goes from 0 to 8 units.

Now let's calculate the values:

1. **sin \(\theta\)** (opposite over hypotenuse):
   \[
   \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{6}{\sqrt{6^2 + 8^2}} = \frac{6}{10} = 0.6
   \]

2. **cos \(\theta\)** (adjacent over hypotenuse):
   \[
   \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{\sqrt{6^2 + 8^2}} = \frac{8}{10} = 0.8
   \]

3. **tan \(\theta\)** (opposite over adjacent):
   \[
   \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{6}{8} = 0.75
   \]

So, the answers are:
- \(\sin \theta = 0.6\)
- \(\cos \theta = 0.8\)
- \(\tan \theta = 0.75\)

Would you like more details on the steps?

Here are 5 related questions:
1. How do we calculate the hypotenuse in any right triangle?
2. What are the trigonometric identities involving \(\sin\) and \(\cos\)?
3. How do we determine the quadrant of \(\theta\) and its impact on signs of \(\sin\), \(\cos\), and \(\tan\)?
4. Can the tangent value ever be greater than 1? If so, when?
5. What is the reciprocal of \(\sin\), \(\cos\), and \(\tan\)?

**Tip:** Always ensure the triangle's orientation when calculating trigonometric ratios to maintain correct signs.

In the following diagram, angle θ is in standard position. In each case, find sin θ, cos θ, and tan θ.

Learn how to find the sine, cosine, and tangent of an angle in standard position. This problem involves trigonometric ratios and applies the Pythagorean theorem to calculate values from a right triangle. Suitable for high school students in Grades 9-12.

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