Question

Tan(-212°)=____.

1. -cot 32°
2. tan 32°
3. cot 32°
4. -tan 32°

Answer 1

4.
`-\tan 32`°

Explanation:

Given:

The tangent of the angle is given as:

`\tan (-212\°)`

Since the angle is negative, it means that it is measured in the clockwise direction as angles measured in clockwise direction are negative and that measured in counter clockwise directions are positive.

-212° when measured from counter clockwise direction will be equal to:

`-212\°(Clockwise)=360-212=148\°(CCW)`

Therefore,
`\tan (-212\°)` =
`\tan (148\°)`

Now, we have the identity for tan as:

`\tan(\pi-\theta)=-\tan \theta`

Here,
`\theta=148\°`

Therefore,

`-\tan (148\°)=\tan(180-148)\\-\tan(148\°)=\tan(32\°)\\\textrm{Multiplying both sides by -1, we get:}\\-1(-\tan(148\°)=-1* \tan(32\°)\\\\\tan(148\°)=-\tan(32\°)`

Hence,
`\tan (-212\°)` =
`\tan (148\°)` =
`-\tan 32`°