It looks like the image shows a right triangle with sides labeled and an angle $\alpha$. We're asked to find the values of $\cos \alpha$ and $\sin \alpha$.

From the image, we have:

• $a = \sqrt{3}$ (the length of the adjacent side),
• $b = 1$ (the length of the opposite side),
• $c$ is the hypotenuse, which we need to calculate.

Using the Pythagorean theorem:

$c^2 = a^2 + b^2$

Substitute $a = \sqrt{3}$ and $b = 1$:

$c^2 = (\sqrt{3})^2 + 1^2 = 3 + 1 = 4$

So,

$c = 2$

Now, we can calculate the trigonometric values:

1. $\cos \alpha = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{c} = \frac{\sqrt{3}}{2}$
2. $\sin \alpha = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{b}{c} = \frac{1}{2}$

Thus:

• $\cos \alpha = \frac{\sqrt{3}}{2}$
• $\sin \alpha = \frac{1}{2}$

Let me know if you need more details or further assistance!

Here are a few questions for deeper exploration:

1. How would the results change if the triangle's sides had different lengths?
2. What are the exact values for $\tan \alpha$ and $\sec \alpha$?
3. How can we calculate the angle $\alpha$ using $\cos \alpha$?
4. Can we use the sine and cosine values to find other trigonometric functions?
5. How would you use the Pythagorean identity to check the accuracy of these results?

Tip: Always double-check the units and ensure you're applying the correct formula, especially in trigonometry where angle measurement units (degrees or radians) matter!