The image you provided contains a mathematical problem involving trigonometry and a right-angled triangle. Let's analyze the problem and solve it step-by-step.

Given Problem:

We have a right triangle with:

• Angle θ.
• Two sides labeled: adjacent side as "x" and opposite side as "y".

The problem appears to ask for the value of a trigonometric function (though the text is partially visible, it looks like cos(θ)).

Solution:

In a right triangle:

1. Cosine (cos) of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{Adjacent Side}}{\text{Hypotenuse}}$

2. Sine (sin) of an angle is the ratio of the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}}$

To calculate cos(θ) using the sides "x" (adjacent) and "y" (opposite), we need to first find the hypotenuse using the Pythagorean theorem: $\text{Hypotenuse} = \sqrt{x^2 + y^2}$

3. Then, the cosine function is given by: $\cos(\theta) = \frac{x}{\sqrt{x^2 + y^2}}$

If "x" and "y" are known, we can compute the exact value of cos(θ).

Conclusion:

Without specific values for "x" and "y", the expression for cos(θ) remains: $\cos(\theta) = \frac{x}{\sqrt{x^2 + y^2}}$

If you need further steps or have any more questions, please let me know!

Would you like more details, or do you have any other questions?

Related Questions:

1. What is the formula for sine, cosine, and tangent in trigonometry?
2. How do you derive the Pythagorean identity for trigonometric functions?
3. How are the trigonometric ratios used in solving real-world problems?
4. How can trigonometric identities simplify expressions?
5. What are some advanced applications of trigonometry in engineering and physics?

Tip: Always remember to consider the unit circle when studying trigonometric functions. It provides a great visual aid to understand how these functions behave!