Do you think there is a value of t for which cos(t)=t?

Question

just started learning about cos(x) and sin(x). having the variable t is no different then x? this is a question my math teacher is asking and i have no idea what she really wants. she asked the question, "do you think there is a value of t for which cos(t)=t?" "yes or no and why?"

Answer 1

The name of the variable doesn't matter, it just represents some quantity.

You could say: "the cosine of something is equal to the same something" but it's much easier to write that as cos(t)=t or cos(x)=x, or use any letter in place of t or x.

Cosine varies between -1 and 1, so t would need to be between the same values. The cosine of a negative number is the same as its positive equivalent, so t would be between 0 and 1. Then it depends on what measurement you use for t. t could be in radians (pure numbers) or degrees (based on there being 360° in a circle). The normal unit is radians for questions of this type. It turns out that t=0.739 approximately.