Question

complete the sentence below. let t be a real number and let p=(a,b) be the point on the unit circle that corresponds to t. then sin t = _ and cos t = _. let t be a real number and let p=(a,b) be the point on the unit circle that corresponds to t. then sin t = □ and cos t = □.

Explanation:

Step1: Recall unit - circle definition

On the unit circle \(x^{2}+y^{2}=1\), for a real number \(t\) and the point \(p=(a,b)\) corresponding to \(t\), the \(x\) - coordinate represents the cosine value and the \(y\) - coordinate represents the sine value.

Step2: Identify sine and cosine values

By the definition of trigonometric functions on the unit circle, \(\sin t = b\) and \(\cos t=a\).

Answer:

\(\sin t = b\), \(\cos t=a\)