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 = _.

Explanation:

Step1: Recall unit - circle definitions

For a point \(p=(a,b)\) on the unit - circle \(x^{2}+y^{2}=1\) corresponding to a real number \(t\), the sine and cosine functions are defined in terms of the coordinates of the point.

Step2: Identify sine and cosine values

By the definition of the sine and cosine functions on the unit - circle, \(\sin t\) is the \(y\) - coordinate of the point \(p\) and \(\cos t\) is the \(x\) - coordinate of the point \(p\).

Answer:

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