The trigonometric functions—sine ($\sin$), cosine ($\cos$), and tangent ($\tan$)—have specific values at $0^\circ$, $180^\circ$, $270^\circ$, and $360^\circ$. These angles correspond to key points on the unit circle. Here's a summary:

$\sin$ Function

• $\sin(0^\circ) = 0$
• $\sin(180^\circ) = 0$
• $\sin(270^\circ) = -1$
• $\sin(360^\circ) = 0$

$\cos$ Function

• $\cos(0^\circ) = 1$
• $\cos(180^\circ) = -1$
• $\cos(270^\circ) = 0$
• $\cos(360^\circ) = 1$

$\tan$ Function

• $\tan(0^\circ) = 0$
• $\tan(180^\circ) = 0$
• $\tan(270^\circ)$ is undefined (since $\cos(270^\circ) = 0$)
• $\tan(360^\circ) = 0$

These values are crucial for solving trigonometric problems, especially those involving periodic functions, angular motion, or wave equations.

Would you like more details on how these values are derived, or do you have any other questions?

Here are 8 related questions you might find interesting:

1. What are the values of the trigonometric functions at $90^\circ$?
2. How do the values of trigonometric functions change in different quadrants?
3. What is the significance of the unit circle in trigonometry?
4. How do you determine the sign of a trigonometric function based on the angle?
5. What are the trigonometric identities involving these angles?
6. How are trigonometric functions used in solving triangles?
7. How does the concept of radians relate to these angles?
8. What are some practical applications of trigonometric functions in real life?

Tip: Remember that the tangent function is undefined when the cosine of the angle is zero. This is because tangent is the ratio of sine to cosine ($\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$).