As `theta` increases from `0^(@)` to `90^(@)`, the value of `cos theta` is

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for statement-I
C. Statement-I is true, Statement-II is false.
D. Statement-I is false and Statement-II is true.

Answer

To solve the question "As `theta` increases from `0^(@)` to `90^(@)`, the value of `cos theta` is", we will analyze the behavior of the cosine function over the specified interval.

### Step-by-Step Solution:

1. **Understanding the Cosine Function**:
The cosine function, denoted as `cos(theta)`, is a trigonometric function that relates the angle `theta` to the ratio of the adjacent side to the hypotenuse in a right triangle.

2. **Range of Theta**:
We are interested in the range of `theta` from `0 degrees` to `90 degrees`.

3. **Values of Cosine at Key Angles**:
- At `theta = 0 degrees`, `cos(0) = 1`.
- At `theta = 90 degrees`, `cos(90) = 0`.

4. **Graphical Representation**:
If we plot the cosine function on a graph:
- The x-axis represents the angle `theta` (from `0` to `90 degrees`).
- The y-axis represents the value of `cos(theta)`.

5. **Behavior of Cosine Function**:
As `theta` increases from `0 degrees` to `90 degrees`, the value of `cos(theta)` decreases:
- Starting from `1` at `0 degrees`, it gradually decreases.
- It reaches `0` at `90 degrees`.

6. **Conclusion**:
Therefore, as `theta` increases from `0 degrees` to `90 degrees`, the value of `cos(theta)` decreases from `1` to `0`.

### Final Answer:
As `theta` increases from `0^(@)` to `90^(@)`, the value of `cos(theta)` decreases from `1` to `0`.

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