The image presents a mathematical statement regarding periodic functions. The problem seems to be asking for definitions related to periodic functions and trigonometric functions like sine and cosine.

Here’s a breakdown of how to complete the blanks:

1. First blank (related to $f(t + p)$):

   • For a periodic function $f$ with period $p$, we have the property: $f(t + p) = f(t) \quad \text{for all} \, t$ So, the correct answer to fill this blank is $f(t)$.

2. Second blank (period of sine and cosine functions):

   • The sine and cosine functions, $y = \sin(x)$ and $y = \cos(x)$, are periodic with a period of $2\pi$. This is because these functions repeat every $2\pi$ radians.

3. Third blank (amplitude of sine and cosine functions):

   • The amplitude of both $\sin(x)$ and $\cos(x)$ is 1, since their maximum value is 1 and their minimum value is -1.

Final Complete Statement:

• "If a function $f$ is periodic with period $p$, then $f(t + p) = f(t)$ for every $t$. The trigonometric functions $y = \sin(x)$ and $y = \cos(x)$ are periodic, with period $2\pi$ and amplitude 1."

Would you like further details on periodic functions, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. What does it mean for a function to have a period?
2. How can you determine the period of a more complex function, such as $y = \sin(2x)$?
3. What is the difference between the amplitude and the period of a trigonometric function?
4. How does the period of a function change when you modify the input (e.g., $\sin(kx)$)?
5. Can you think of examples of periodic functions outside of trigonometry?

Tip: When determining the period of a function, always check the interval after which the function repeats its values. For trigonometric functions, this interval is typically based on $2\pi$.