The trigonometric functions for arbitrary angles

Question 1

What is sin v equal to on the unit circle?

Answer 1

sin (v + n*2π) for all n ∈ Z

Question 2

What is Z?

Answer 2

All integers; all whole numbers including zero i.e. Zahlen

Question 3

What is cos v equal to on the unit circle?

Answer 3

cos (v+n*2π) for all n ∈ Z

Question 4

What is sin 0?

Answer 4

0

Question 5

What is sin π/2?

Answer 5

1

Question 6

What is sin π?

Answer 6

0

Question 7

What is sin 3π/2?

Answer 7

-1

Question 8

What is sin 2π?

Answer 8

0

Question 9

What is cos 0?

Answer 9

1

Question 10

What is cos π/2?

Answer 10

0

Question 11

What is cos π?

Answer 11

-1

Question 12

What is cos 3π/2?

Answer 12

0

Question 13

What is cos 2π?

Answer 13

1

Question 14

What is tan 0?

Answer 14

0

Question 15

What is tan π/2?

Answer 15

undefined

Question 16

What is tan π?

Answer 16

0

Question 17

What is tan 3π/2?

Answer 17

undefined

Question 18

What is tan 2π?

Answer 18

0

Question 19

What is cot 0?

Answer 19

undefined

Question 20

What is cot π/2?

Answer 20

0

Question 21

What is cot π?

Answer 21

undefined

Question 22

What is cot 3π/2?

Answer 22

0

Question 23

What is cot 2π?

Answer 23

undefined

Question 24

What values can sin v be?

Answer 24

-1 ≤ sin v ≤ 1

Question 25

What values can cos v be?

Answer 25

-1 ≤ cos v ≤ 1

Question 26

What signs (±) does sin v have in the different quadrants?

Answer 26

Positive in first and second quadrant, Negative in third and fourth quadrant.

Question 27

What signs (±) does cos v have in the different quadrants?

Answer 27

Positive in first and fourth quadrant, Negative in second and third quadrant.

Question 28

What signs (±) does tan v have in the different quadrants?

Answer 28

Positive in first and third quadrant, Negative in second and fourth quadrant.

Question 29

What signs (±) does cot v have in the different quadrants?

Answer 29

Positive in first and third quadrant, Negative in second and fourth quadrant.