Question

what is the sin, cos, tan, csc, sec, and cot of 0 degrees?

Answer 1

Do you have a unit circle with you?

Answer 2

yes

Answer 3

ok locate the angle 0 degrees

what is the corresponding point on the unit circle?

Answer 4

1,0 ?

Answer 5

use parenthesis

but yeah, (1,0)

Answer 6

the x coordinate is equal to cos(theta)

the y coordinate is equal to sin(theta)

Answer 7

so this means `cos(0) = 1` and `sin(0) = 0`

Answer 8

tan(0)= 0?

Answer 9

to compute `tan(0)` you use this trig identity

\[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

Answer 10

yeah you'll find that tan(0) = sin(0)/cos(0) = 0/1 = 0

Answer 11

for the other three, use the identities listed on page 2 under the "Reciprocal Identities" section

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 12

eg: csc(x) = 1/(sin(x))

Answer 13

csc(0)= 0?

Answer 14

what was sin(0) equal to again?

Answer 15

0

Answer 16

so

csc(x) = 1/(sin(x))
csc(0) = 1/(sin(0))
csc(0) = 1/0
csc(0) = UND or NaN


UND = undefined
NaN = Not a Number

Answer 17

1/0 is NOT the same as 0/1

0/1 = 0
1/0 is undefined because you can't have 0 in the denominator

Answer 18

so i put undefined?

Answer 19

yeah

Answer 20

for csc(0)

Answer 21

and for sec i also put undefined

Answer 22

why? what was cos(0) ?

Answer 23

1

Answer 24

take the reciprocal of that to find sec(0)

Answer 25

another way to view why csc(0) was undefined is that 0 doesn't have a reciprocal

however, sec(0) is defined

Answer 26

1?

Answer 27

yeah sec(0) = 1

Answer 28

cot(0)= undefined?

Answer 29

why?

Answer 30

tan(0)=0

Answer 31

good, and taking the reciprocal of 0 leads to undefined

Answer 32

so to summarize

sin(0) = 0
cos(0) = 1
tan(0) = 0

csc(0) = und
sec(0) = 1
cot(0) = und

Answer 33

thanks.

Answer 34

np