To evaluate \( g(5\pi/3) \), we need to substitute \( t = 5\pi/3 \) into the function \( g(t) = \cos(t) \).

So,
\[
g(5\pi/3) = \cos(5\pi/3)
\]

Now, let's evaluate \( \cos(5\pi/3) \):

- The angle \( 5\pi/3 \) is in the fourth quadrant (since it is between \( 2\pi \) and \( 3\pi/2 \)).
- In the fourth quadrant, the cosine function is positive.
- \( 5\pi/3 \) is co-terminal with \( \pi/3 \), meaning \( \cos(5\pi/3) = \cos(\pi/3) \).
- \( \cos(\pi/3) = 1/2 \).

Thus, 
\[
g(5\pi/3) = \frac{1}{2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the value of \( \sin(5\pi/3) \)?
2. How do we convert radians to degrees, and what is \( 5\pi/3 \) in degrees?
3. What are the values of the cosine function in different quadrants?
4. Can you explain why cosine is positive in the fourth quadrant?
5. What is the unit circle and how does it help with trigonometric functions?

**Tip:** In trigonometry, the unit circle is a useful tool to quickly determine the values of sine and cosine for common angles.

g(t) = cos(t); t = 5π/3. What is g(5π/3)?

Discover how to evaluate g(5π/3) using the cosine function. This problem involves key trigonometric concepts like the unit circle and the cosine function's behavior in different quadrants. Follow a step-by-step solution suitable for students in Grades 10-12.

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