Trigonometric Functions

• anpanman

  3 Sep 08, 22:19

  Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

   

  Can anyone tell me what the question means when it says,"opposite signs"?

   

  Below is another question which I do not understand. Please take a look. (=

   

  Given that sin 20 deg = k, express the following in terms of k.

   

  i.tan(-20deg)

  ii. sin 70 deg.

   

  I think I just need help for part (i) of the question. I will attempt the second part on my own though.

   

  Thanks for reading!

• ^tamago^

  3 Sep 08, 22:31

  Originally posted by anpanman:

  Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

   

  Can anyone tell me what the question means when it says,"opposite signs"?

  
  

  tan A = sin A/cos A. If cos A and tan A can have opposite signs, it means there are solutions in all 4 quadrants since cos A can be positive or negative.

  tan A = opp / adj = - 5 / 12.
  hyp² = opp² + adj² = 5² + 12² = 13². ==> hyp = 13
  cos A = adj / hyp = ± 12 / 13

  cos (π/2 - A) = sin A = opp / hyp = ± 5 / 13

• ^tamago^

  3 Sep 08, 22:40

  Originally posted by anpanman:

  Given that sin 20º = k, express the following in terms of k.

   

  i. tan (-20º)

  ii. sin 70º.

  
  
  
  
• wishboy

  4 Sep 08, 01:36

  Originally posted by anpanman:

  Given that tan A = - 5 /12 and that tan A and cos A have opposite signs, find the value of cos A and of cos (pi/2 - A).

  Can anyone tell me what the question means when it says,"opposite signs"?

  opposite signs mean that if one is +ve, the other is -ve, and vice versa.

  tan A = -5/12 (angle A falls in 2nd or 4th quadrant)

  since they say tan A and cos A have opposite signs,
  cos A is +ve (angle A falls in 1st or 4th quadrant)

  so now u noe tat angle A is in the 4th quadrant

  opp. = 5, adj. = 12, hyp. = 13

  cos A = 12/13

  cos (pi/2 - A)
  = sin A (which is -ve since A is in the 4th quadrant)
  = -5/13

  someone can confirm whether mi or tamago is correct?

• bonkysleuth

  4 Sep 08, 08:23

  wishboy is correct. ^tamago^'s way of deriving the answer isn't wrong too. But he has to eliminate one of the signs (+ / -) since the answer isn't going to really be lying in all 4 quadrants.

   

  By the way, towards the end where wishboy tried to find the answer for cos(pi/2 -A) = sin A, did you do so using the complementary angle formula? where cos x = sin (90 - x)? may i know why we can apply this formula here? how do you know it is a complementary angle without the question telling us so?

   

  Thanks lots.

   

   

• ^tamago^

  4 Sep 08, 11:32

  Originally posted by wishboy:

  opposite signs mean that if one is +ve, the other is -ve, and vice versa.

  tan A = -5/12 (angle A falls in 2nd or 4th quadrant)

  since they say tan A and cos A have opposite signs,
  cos A is +ve (angle A falls in 1st or 4th quadrant)

  so now u noe tat angle A is in the 4th quadrant

  
  yours correct. misinterpret the word "can have" instead of "is", and forgot tan A is -ve so only left 2 quadrants. paiseh.