Question

Inverse trig question

Answer 1

Why does arctan(-sqrt3) equal -pi/3 instead of 5pi/3?

Answer 2

Arccos(-1/2) equals 2pi/3...

Answer 3

Because negative indicates you're moving clockwise instead of anticlockwise

Answer 4

What's the difference though?

Answer 5

Difference between what?

Answer 6

If tan(5pi/3) equals -sqrt3, why isn't 5pi/3 the answer?

Answer 7

Well because trigonometric functions can give many values for one input like
arccos 0 =1/2 pi , 2.5pi, 5 pi and so on

Answer 8

Sorry, I'm not following...
Are you saying that 5pi/3 would have multiple values?

Answer 9

I am saying arctan(-sqrt3) has many values

Answer 10

The relation has many values, but the function only has one value doesn't it? :/

Answer 11

It should have a capital A.. which means the function of inverse tangent, not the relation..

Answer 12

Is the range for the angle defined?

Answer 13

This is the actual question:
Evaluate the expression Arctan(-sqrt3). Give the exact value.
And the answer was -pi/3 I'm trying to understand why it was -pi/3 instead of 5pi/3

Answer 14

No, it doesn't specify a range. But the capital A means the range is restricted.

Answer 15

Well both answer are correct
But remember a property
tan (-theta) = -tan(theta)

Answer 16

Well both answer are correct
But remember a property
arctan (-theta) = -arctan(theta)

Answer 17

Are there different properties for cos and sin?

Answer 18

Because Arccos(-1/2) is 2pi/3, not a negative number....

Answer 19

well imagine if we made the restriction 1st and 4th quadrant for tangent.
That would look kind of awkward, wouldn't it?