anonymous
  • anonymous
what is the sin, cos, tan, csc, sec, and cot of 0 degrees?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
Do you have a unit circle with you?
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
ok locate the angle 0 degrees what is the corresponding point on the unit circle?

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anonymous
  • anonymous
1,0 ?
jim_thompson5910
  • jim_thompson5910
use parenthesis but yeah, (1,0)
jim_thompson5910
  • jim_thompson5910
the x coordinate is equal to cos(theta) the y coordinate is equal to sin(theta)
jim_thompson5910
  • jim_thompson5910
so this means `cos(0) = 1` and `sin(0) = 0`
anonymous
  • anonymous
tan(0)= 0?
jim_thompson5910
  • jim_thompson5910
to compute `tan(0)` you use this trig identity \[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]
jim_thompson5910
  • jim_thompson5910
yeah you'll find that tan(0) = sin(0)/cos(0) = 0/1 = 0
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
eg: csc(x) = 1/(sin(x))
anonymous
  • anonymous
csc(0)= 0?
jim_thompson5910
  • jim_thompson5910
what was sin(0) equal to again?
anonymous
  • anonymous
0
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
so i put undefined?
jim_thompson5910
  • jim_thompson5910
yeah
jim_thompson5910
  • jim_thompson5910
for csc(0)
anonymous
  • anonymous
and for sec i also put undefined
jim_thompson5910
  • jim_thompson5910
why? what was cos(0) ?
anonymous
  • anonymous
1
jim_thompson5910
  • jim_thompson5910
take the reciprocal of that to find sec(0)
jim_thompson5910
  • jim_thompson5910
another way to view why csc(0) was undefined is that 0 doesn't have a reciprocal however, sec(0) is defined
anonymous
  • anonymous
1?
jim_thompson5910
  • jim_thompson5910
yeah sec(0) = 1
anonymous
  • anonymous
cot(0)= undefined?
jim_thompson5910
  • jim_thompson5910
why?
anonymous
  • anonymous
tan(0)=0
jim_thompson5910
  • jim_thompson5910
good, and taking the reciprocal of 0 leads to undefined
jim_thompson5910
  • jim_thompson5910
so to summarize sin(0) = 0 cos(0) = 1 tan(0) = 0 csc(0) = und sec(0) = 1 cot(0) = und
anonymous
  • anonymous
thanks.
jim_thompson5910
  • jim_thompson5910
np

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