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{ = }(1)/(tg(\theta))=\frac{1}{\frac{sen(\theta)}{\text{cos(}\theta)}} \\ \text{cot(}\theta)\text{ = }(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)=(0)/(-1) \\ \tan (\theta)=0 \end{gathered}`

The cossec is the inverse of the sine.

The sec is the inverse of the cossine.

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