Question

use the unit circle to find the value of each trigonometric function at the angle indicated. cos(270°)= sin(270°)= -1 tan(270°)= 0 cos(0°)= 1 sin(0°)= tan(0°)=

Explanation:

Step1: Recall unit - circle definitions

On the unit circle, for an angle \(\theta\), \(\cos\theta=x\) - coordinate of the point on the unit circle corresponding to \(\theta\), \(\sin\theta = y\) - coordinate of the point on the unit circle corresponding to \(\theta\), and \(\tan\theta=\frac{\sin\theta}{\cos\theta}\).

Step2: Find values for \(\theta = 270^{\circ}\)

For \(\theta = 270^{\circ}\), the point on the unit circle is \((0,-1)\). So, \(\cos(270^{\circ})=0\), \(\sin(270^{\circ})=-1\), and \(\tan(270^{\circ})=\frac{\sin(270^{\circ})}{\cos(270^{\circ})}=\frac{-1}{0}\) (undefined).

Step3: Find values for \(\theta = 0^{\circ}\)

For \(\theta = 0^{\circ}\), the point on the unit circle is \((1,0)\). So, \(\cos(0^{\circ}) = 1\), \(\sin(0^{\circ})=0\), and \(\tan(0^{\circ})=\frac{\sin(0^{\circ})}{\cos(0^{\circ})}=\frac{0}{1}=0\).

Answer:

\(\cos(270^{\circ}) = 0\), \(\sin(270^{\circ})=-1\), \(\tan(270^{\circ})\) is undefined, \(\cos(0^{\circ}) = 1\), \(\sin(0^{\circ})=0\), \(\tan(0^{\circ}) = 0\)