As `theta` increases from `0^(@)` to `90^(@)`, the value of `sin theta` : -

Options

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

Answer

To solve the question "As θ increases from 0° to 90°, what happens to the value of sin θ?", we can follow these steps:

### Step 1: Understanding the Sine Function
The sine function, sin θ, is a trigonometric function that relates the angle θ to the ratio of the length of the opposite side to the hypotenuse in a right triangle.

### Step 2: Analyzing the Range of θ
We are interested in the behavior of sin θ as θ increases from 0° to 90°.

### Step 3: Evaluating sin θ at Key Angles
- At θ = 0°, sin(0°) = 0
- At θ = 90°, sin(90°) = 1

### Step 4: Observing the Behavior of sin θ
As θ increases from 0° to 90°, we can observe:
- The value of sin θ starts at 0 when θ = 0°.
- The value of sin θ reaches its maximum of 1 when θ = 90°.

### Step 5: Conclusion
From the analysis, we conclude that as θ increases from 0° to 90°, the value of sin θ increases continuously from 0 to 1.

### Final Answer
Thus, the value of sin θ increases as θ increases from 0° to 90°.

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