Question

find tan(7pi/4)

Answer 1

How well do you know the unit circle? I only ask because the more you know the easier this is :P Wanna know where to start off.

Answer 2

I am very familiar with the Unit circle haha

Answer 3

i just need to refresh on how to do this, i kind of forgot how to do it during summer :/

Answer 4

Alright then, haha. Well, you should know that pi/4, 3pi/4 5pi/4 and 7pi/4 have thesame sin and cos value, except the sign changes depending on the quadrant. Both would be some sign of sqrt(2)/2.

That being said, tangent is sin/cos. So if tan = sin/cos and sin and cos at those pi/4 values are the same, then we know that we will either get 1 or -1 when we take the tangent. Make sense so far?

Answer 5

yeah

Answer 6

So now all we need to know is what quadrant 7pi/4 is in. A full circle is going to be 2pi or the same as 8pi/4. So 7pi/4 is going to be merely 1/8th of the circle before that.



So that's in the 4th qudrant, right? So doyou get negative or positive 1 in that quadrant?

Answer 7

Negative 1?

Answer 8

yep :P So thats your answer.

Answer 9

tan7pi/4 = -1 ?

Answer 10

yep :3

Answer 11

im sorry but is there an equation i can do to find this?

Answer 12

using SohCahToa or something

Answer 13

Well, without using a calculator, it's just knowledge of the unit circle that you needto have really. Soh Cah Toa just shows you in a different way how sin/cos = tan. But even then, you still would need to know the appropriate values based on the angle. I couldn't say there's a flat out formula for knowing those values. I personally have a trick that helps me remember the sin and cos values on theunit circle, though.

Answer 14

oh okay, Thank you so much! :) but would you mind sharing that trick?

Answer 15

Yeah, that's fine, just gotta give me a second to drawit. It's mainly a pattern :3