What is tan 11/6? Math

A

Step-by-step explanation:

So every time I see a question like this I like to relate it to first quadrant values and then work my way back.

So we have tan(11pi/6)

We can look at this as .

Basically we can find the value for tan(pi/6) as a first quadrant value and then multiply that angular value by 11 to see what we get. I'll show you what I mean. If you have your unit circle memorized you know that pi/6 = 30 degrees. You also know that tan(pi/6) or tan(30) is equal to

So thats our answer and now we have to figure out whether this will be negative or positive based on our angle value of tangent. So we have 11 times pi/6.

We can think of this as 11 x 30 degrees

This is equal to 330 degrees!

This means that this value is in the fourth quadrant. In the fourth quadrant sine values are negative so the overall value should be negative so our final answer is:

tan(11pi/6) =

You can apply this same logic with all other values so like if you had sin(11pi/6) you could say well sin(pi/6) = 1/2 so thats our value and we know that 11 x 30 = 330 which means we are in the fourth quadrant so sin(11pi/6) = -1/2.

Hope this helps.