Question

A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t. The point P is (√10/10 , -3√10/10) sin t=cos t= tan t=csc t=sec t=cot t=

Answer 1

Given

Graph

Procedure

Point P

$P=(\frac{\sqrt[]{10}}{10},-\frac{3\sqrt[]{10}}{10})$

Let's calculate the swept angle

$\begin{gathered} \sin \theta=\frac{\frac{3\sqrt[]{10}}{10}}{1} \\ \sin \theta=\frac{3\sqrt[]{10}}{10} \\ \theta=\sin ^{-1}(\frac{3\sqrt[]{10}}{10}) \\ \theta=71.56\text{ \degree} \end{gathered}$

Now the angle swept by t is

$\begin{gathered} t=360-\theta \\ t=288.44\text{ \degree} \end{gathered}$$\begin{gathered} \sin (288.44)=-0.948 \\ \cos (288.44)=0.3163 \\ \tan (288.44)=-2.999 \\ \end{gathered}$$\begin{gathered} \csc (288.44)=-1.054 \\ \sec (288.44)=3.1614 \\ \cot (288.44)=-0.333 \end{gathered}$