anonymous
  • anonymous
check answer please! Let theta be an angle in quadrant III such that sin (theta)= (-3/4). Find the exact values of and sec and cot. i got sec=-4/√7 and cot=√7/-3
Mathematics
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schrodinger
  • schrodinger
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Jhannybean
  • Jhannybean
\(\sin(\theta) = -\dfrac{3}{4}\) sin = opp/ hyp yes?
Nnesha
  • Nnesha
if you remember CAST rule which function is positive or negative in 3rd quadrant ?
Nnesha
  • Nnesha
the*

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anonymous
  • anonymous
cos and sin are negative while tan is positive
Jhannybean
  • Jhannybean
|dw:1439527075496:dw|
Nnesha
  • Nnesha
so if tan is positive cot = ? positive or negative ?
anonymous
  • anonymous
negative?
Nnesha
  • Nnesha
tan is reciprocal of cot
Nnesha
  • Nnesha
i just wanted to know if you understood the signs of all 3 functions or not
Nnesha
  • Nnesha
look at jhanny;s comment answer that she will help you
anonymous
  • anonymous
I got adjacent as √7 and opposite as -3
Nnesha
  • Nnesha
|dw:1439527747421:dw| write the opposite and hyp
anonymous
  • anonymous
opposite is -3 and hyp is -4
Nnesha
  • Nnesha
-4 ??
anonymous
  • anonymous
maybe im confused, but doesnt the negative sign apply to both 3 and 4?
Nnesha
  • Nnesha
well if both hyp and opposite are negative then it should be \[\frac{ -3 }{ -4 } \] which is equal to positive
anonymous
  • anonymous
oh so opposite would be -3 and hyp would just be 4
Nnesha
  • Nnesha
yes right |dw:1439527997509:dw| and adjacent equal to ?
anonymous
  • anonymous
√7
Nnesha
  • Nnesha
\(\color{blue}{\text{Originally Posted by}}\) @Kimes I got adjacent as √7 and opposite as -3 \(\color{blue}{\text{End of Quote}}\) yes right
anonymous
  • anonymous
so sec is 4/√7 and cot is √7/-3
Nnesha
  • Nnesha
no cot = ? wait a sec
anonymous
  • anonymous
√7/3?
Nnesha
  • Nnesha
yes cot should be positive
anonymous
  • anonymous
oh gosh, gotta study more on this, thanks again!
Nnesha
  • Nnesha
sec = ??
anonymous
  • anonymous
oh its not 4/√7?
anonymous
  • anonymous
oh wait -4/√7
Nnesha
  • Nnesha
remember what i told you on previous thread
Nnesha
  • Nnesha
yes right cos sec should be negative but what else
Nnesha
  • Nnesha
something about radical sign
anonymous
  • anonymous
oh multiply, so it'll be -4√7/7
Nnesha
  • Nnesha
yep
anonymous
  • anonymous
thank you so much!
Nnesha
  • Nnesha
np

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