Question

Cot (0) is undefined, pie/2 < or equal to (0) < or equal to 3pie/2Trig: find the exact values of the remaining trigonometric functions of (0) satisfying the given conditions. ( If an answer is undefined, enter undefined)Cos(0)=Sec(0)=

Answer 1

The cotangent of a number is given by:

$\begin{gathered} \text{cot(}\theta)\text{ = }\frac{1}{tg(\theta)}=\frac{1}{\frac{sen(\theta)}{\text{cos(}\theta)}} \\ \text{cot(}\theta)\text{ = }\frac{cos(\theta)}{\sin (\theta)} \end{gathered}$

Since the value of the cotangent is undefined, the value of the sine must be equal to 0. Thefore:

$\sin (\theta)=0$

We know that when the sine of an angle is equal to 0, its cosine is equal to 1 or -1. Since the interval is from pi/2 to 3pi/2. Thefore:

$cos(\theta)=-1$

The tangent is the division between the sine and cosine.

$\begin{gathered} \tan (\theta)=\frac{0}{-1} \\ \tan (\theta)=0 \end{gathered}$

The cossec is the inverse of the sine.

$\text{cos}\sec \text{(}\theta)\text{ = }\frac{1}{\sin (\theta)}=\frac{1}{0}\text{ = undefined}$

The sec is the inverse of the cossine.

$\text{sec(}\theta)=\frac{1}{\text{cos(}\theta)}=\frac{1}{-1}=-1$