MATH SOLVE

4 months ago

Q:
# What is the value of tan (-2pi/3)?the correct answer is sqrt 3 but how do i get that? someone explain

Accepted Solution

A:

This revolves around exact trig values - no easy way to say this, you just need to memorise them. They are there for sin cos and tan, but I will give you the main tan ones below - note this is RADIANS (always work in them when you can, everything is better):

tan0: 0

tanpi/6: 1/sqrt(3)

tanpi/4: 1

tanpi/3: sqrt(3)

tanpi/2: undefined

Now we just need to equate -2pi/3 to something we understand. 2pi/3 is 1/3 of the way round a circle, so -2pi/3 is 1/3 of the way round the circle going backwards (anticlockwise), so on a diagram we already know it's in the third quadrant of the circle (somewhere between pi and 3pi/2 rads).

We also know it is pi/3 away from pi, so we are looking at sqrt(3) or -sqrt(3) because of those exact values.

Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).

tan0: 0

tanpi/6: 1/sqrt(3)

tanpi/4: 1

tanpi/3: sqrt(3)

tanpi/2: undefined

Now we just need to equate -2pi/3 to something we understand. 2pi/3 is 1/3 of the way round a circle, so -2pi/3 is 1/3 of the way round the circle going backwards (anticlockwise), so on a diagram we already know it's in the third quadrant of the circle (somewhere between pi and 3pi/2 rads).

We also know it is pi/3 away from pi, so we are looking at sqrt(3) or -sqrt(3) because of those exact values.

Now we just need to work out if it's positive or negative. You can look up a graph of tan and it'll show that the graph intercepts y at (0,0) and has a period of pi rads. Therefore between pi and 3pi/2 rads, the values of tan are positive. Therefore, this gives us our answer of sqrt(3).