To find the value of each of the six trigonometric functions of an angle $\theta$, we need to know the lengths of the sides of a right triangle or the coordinates of a point on the terminal side of the angle in standard position.

The six trigonometric functions for an angle $\theta$ are defined as follows, assuming a right triangle with an angle $\theta$:

1. Sine ($\sin\theta$): $\frac{\text{opposite}}{\text{hypotenuse}}$
2. Cosine ($\cos\theta$): $\frac{\text{adjacent}}{\text{hypotenuse}}$
3. Tangent ($\tan\theta$): $\frac{\text{opposite}}{\text{adjacent}}$
4. Cosecant ($\csc\theta$): $\frac{\text{hypotenuse}}{\text{opposite}}$ or $\frac{1}{\sin\theta}$
5. Secant ($\sec\theta$): $\frac{\text{hypotenuse}}{\text{adjacent}}$ or $\frac{1}{\cos\theta}$
6. Cotangent ($\cot\theta$): $\frac{\text{adjacent}}{\text{opposite}}$ or $\frac{1}{\tan\theta}$

Solution Approach

To calculate these values, we need:

• Either the side lengths of a right triangle
• Or the coordinates of a point on the terminal side of the angle $\theta$

Request for Additional Information

Please provide:

• A description of the figure, such as side lengths or coordinates of a point related to the angle $\theta$.
• A clear image of the figure for accurate calculation.

Once you provide this information, I can calculate the values of all six trigonometric functions for angle $\theta$.

Would you like to proceed by providing more details or uploading an image?

Follow-up Questions:

1. Do you have a specific figure or right triangle in mind?
2. Are the coordinates of a point on the unit circle provided?
3. Is there any information about the quadrant where angle $\theta$ lies?
4. Do you need the values of the trigonometric functions in a specific form (exact, decimal)?
5. Are there any constraints or conditions for the angle $\theta$ in the problem?

Tip:

To solve trigonometry problems effectively, always start by identifying the triangle's sides or the coordinates in relation to the angle in question.