Question

Solve for tangent x= -1 in radians without a calculator

Answer 1

`x\text{ = }(3)/(4)\pi\text{ or }(7)/(4)\pi`

Step-by-step explanation:

Here, we want to calculate the value of x without using a calculator

We have to look for the quadrants where the tan is negative

These are the second and the fourth quadrant

On the second quadrant, we have the reference angles as:

`180-x`

Mathematically in degrees:

`\begin{gathered} \text{if tan x = 1} \\ x\text{ = 45 deg} \end{gathered}`

Now, on the second quadrant, we have it that:

`180-45\text{ = 135 deg}`

On the fourth quadrant, we have the reference angle calculated as:

`\begin{gathered} 360-\theta \\ \theta\text{ = 360-45} \\ \theta\text{ = 315 deg} \end{gathered}`

Lastly, we have to convert these angles to radians

Mathematically, 1 pi is 180 degrees:

`\begin{gathered} 1\text{ }\pi=\text{ 180 deg} \\ x\text{ = 135 deg} \\ x\text{ = }(135\pi)/(180)\text{ = }(3)/(4)\pi \\ \\ \text{Lastly:} \\ 1\pi\text{ = 180 deg} \\ x\text{ = 315 deg } \\ \\ x\text{ = }(315)/(180)\pi\text{ = }(7)/(4)\pi \end{gathered}`