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The problem in your image asks to find the sine of an angle \(\theta\), whose terminal side passes through the point \((0.40, 0.09)\). The goal is to calculate \(\sin \theta\).

To solve this, follow these steps:

### Step 1: Use the Pythagorean theorem to find the hypotenuse.
Given a point \((x, y)\), the hypotenuse \(r\) is the distance from the origin to the point, which is calculated as:

\[
r = \sqrt{x^2 + y^2}
\]

Substituting the values \(x = 0.40\) and \(y = 0.09\):

\[
r = \sqrt{(0.40)^2 + (0.09)^2} = \sqrt{0.16 + 0.0081} = \sqrt{0.1681}
\]
\[
r = 0.41
\]

### Step 2: Calculate \(\sin \theta\).
The sine of an angle is given by:

\[
\sin \theta = \frac{y}{r}
\]

Substitute \(y = 0.09\) and \(r = 0.41\):

\[
\sin \theta = \frac{0.09}{0.41} \approx 0.2195
\]

Thus, \(\sin \theta \approx 0.2195\).

Would you like further details or have any questions?

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Here are some additional related questions you might find helpful:
1. How do you calculate \(\cos \theta\) and \(\tan \theta\) for this problem?
2. What are the other trigonometric functions (sec, csc, cot) for this point?
3. How do you determine the quadrant of the angle based on the point coordinates?
4. What is the geometric interpretation of trigonometric functions using this point?
5. Can you find the reference angle for this \(\theta\)?

**Tip:** Always double-check your arithmetic when working with decimals in trigonometry. It can affect the accuracy of your final answer.

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point (0.40, 0.09).

Learn how to find the sine of an angle θ whose terminal side passes through the point (0.40, 0.09). This problem involves trigonometry, including using the Pythagorean theorem and sine function.

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