Question

Hi! Good morning, can you help me to evaluate (if Possible) the six trigonometric functions of the Rea number, please!!!

Answer 1

We can evaluate the six trigonometric functions for t = -7π/4.

First, we start by transforming it into a positive angle, adding a full circle (2π):

`t=-(7\pi)/(4)+2\pi=-(7)/(4)\pi+(8)/(4)\pi=(\pi)/(4)`

Now, we can evaluate the basic 3 trigonometric functions as:

`\begin{gathered} \sin (t)=\frac{\sqrt[]{2}}{2} \\ \cos (t)=\frac{\sqrt[]{2}}{2} \\ \tan (t)=(\sin(t))/(\cos(t))=\frac{\frac{\sqrt[]{2}}{2}}{\frac{\sqrt[]{2}}{2}}=1 \end{gathered}`

and the other 3 can be evaluated as:

`\begin{gathered} \csc (t)=(1)/(\sin(t))=\frac{2}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{2\sqrt[]{2}}{2}=\sqrt[]{2} \\ \sec (t)=(1)/(\cos(t))=\sqrt[]{2} \\ \cot (t)=(1)/(\tan (t))=1 \end{gathered}`

Answer: if t = -7π/4, we have

sin(t) =√2/2

cos(t) = √2/2

tan(t) = 1

csc(t) =√2

sec(t) =√2

cot(t) = 1