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Trigonometric Functions

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  • anpanman
    anpanman's Avatar
    52 posts since Aug '08
    • 03 Sep `08, 10:19PM

      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!

  • Moderator
    ^tamago^
    ★.
    ^tamago^'s Avatar
    51,105 posts since Sep '03
    • 03 Sep `08, 10:31PM
      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

  • Moderator
    ^tamago^
    ★.
    ^tamago^'s Avatar
    51,105 posts since Sep '03
    • 03 Sep `08, 10:40PM
      Originally posted by anpanman:

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

       

      i. tan (-20º)

      ii. sin 70º.


      image
      image

  • wishboy
    wishboy's Avatar
    1,269 posts since Aug '05
    • 04 Sep `08, 1:36AM
      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
    bonkysleuth's Avatar
    314 posts since Mar '07
    • 04 Sep `08, 8:23AM

      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.

       

       

  • Moderator
    ^tamago^
    ★.
    ^tamago^'s Avatar
    51,105 posts since Sep '03
    • 04 Sep `08, 11:32AM
      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.

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