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Math Help - trigonometrical qn

  1. #1
    Member maybeline9216's Avatar
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    Red face trigonometrical qn

    Given that cot q=-t, t>0 and 0 q180 , find, in terms of t,

    (a) cosec q
    (b) tan(-q)
    (c) sin(90-q )

    for(b) is it -(-1/t) = -(1/-t) ?? im kinda confused....

    also can anyone tell me how to derive the following formulas from the four quadrants mtd....(as i dun want to memorise the formulas)

    1) cos(-x)=cos x
    2) tan(-x) = -tan x
    3)sin(90-x)=cos x
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  2. #2
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    Quote Originally Posted by maybeline9216 View Post
    Given that cot q=-t, t>0 ≤q≤180 , find, in terms of t,
    (a) cosec q
    (b) tan(-q)
    (c) sin(90-q)

    for(b) is it -(-1/t) = -(1/-t) ?? im kinda confused....
    for (b), -(-1/t)=1/t.

    For (a), remember the formula \cot^2(x)+1=\text{cosec}^2(x)

    For (c), note that \sin(90^\circ-x)=\cos(x). Then, \cot(x)=\frac{\cos(x)}{\sin(x)}=\cos(x) \cdot \text{cosec}(x) \implies \cos(x)=\frac{\cot(x)}{\text{cosec}(x)}

    also can anyone tell me how to derive the following formulas from the four quadrants mtd....(as i dun want to memorise the formulas)
    These formula are correct in whatever quadrant x is.

    1) cos(-x)=cos x
    2) tan(-x) = -tan x
    3)sin(90-x)=cos x
    Draw a circle. Take a point x of the circle in quadrant 1 (it's in general easier). Remember that its abscissa is cos(x) and its ordinate is sin(x).
    After that, find on the circle where -x is, that is to say the point forming an opposite angle comparing to x.
    Find where 90-x is, etc... It's the way to remember that (yes, because you'll have to remember these formula, no matter what you want )
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  3. #3
    Member maybeline9216's Avatar
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    Question

    Opps...sorry i forgot to mention how to derive the following formulas from the four quadrant

    For any angle x(whether acute or obtuse,i just dun understand the obtuse part)

    For sin(-x) = -sin x (i understand because for the 3rd and 4th quadrant,sine is negative)

    But i dun understand why
    1) cos(-x)=cos x
    2) tan(-x) = -tan x
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