Question

Can the sine or the cosine function ever equal 5? Why or why not?

Answer 1

Sin and cos functions can never be equal to 5. They can never be greater than 1! Both!

You can think of sin and cos functions as projections (that is how i do). Imagine xy coordinate system. Draw a circle which center (center of circle) is in center of xy coordinate system. Let radius of that circle be one (you can take one to be any length you want). 
Now, x - axis and any radius of that circle make an angle. 
NOW HERE IS IMPORTANT PART:
-projection of that radius on x-axis is cosine of the angle that radius and x-axis make.
-projection of that radius on y-axis is sinus of the angle that radius and x-axis make.

From that you can see that projections cannot ever be greater than 1.

Answer 2

No, they cant!!! They are anti- of each other. So, they will be equal to 1 only and not other than that....