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

Options

A. Increases
B. Decreases
C. Remains constant
D. First decrease then increases.

Answer

To analyze how the value of \( \cos \theta \) changes as \( \theta \) increases from \( 0^\circ \) to \( 90^\circ \), we can follow these steps:

### Step 1: Understand the cosine function
The cosine function is defined on the unit circle. For any angle \( \theta \), \( \cos \theta \) represents the x-coordinate of the point on the unit circle corresponding to that angle.

### Step 2: Evaluate \( \cos \theta \) at key points
- At \( \theta = 0^\circ \):
\[ \cos 0^\circ = 1 \]
- At \( \theta = 90^\circ \):
\[ \cos 90^\circ = 0 \]

### Step 3: Analyze the behavior of \( \cos \theta \) as \( \theta \) increases
As \( \theta \) increases from \( 0^\circ \) to \( 90^\circ \), the value of \( \cos \theta \) decreases from 1 to 0. This indicates that \( \cos \theta \) is a decreasing function in this interval.

### Step 4: Graph the function
To visualize this, we can sketch the graph of \( \cos \theta \):
- The graph starts at the point (0, 1) when \( \theta = 0^\circ \).
- As \( \theta \) approaches \( 90^\circ \), the graph descends to the point (90, 0).

### Conclusion
Thus, as \( \theta \) increases from \( 0^\circ \) to \( 90^\circ \), the value of \( \cos \theta \) decreases from 1 to 0.

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