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Thread: [SOLVED] Tignometry Help

  1. #1
    Member looi76's Avatar
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    [SOLVED] Tignometry Help

    Question:
    Use the symmetric and periodic properties of the sine, cosine and tangent functions to establish the following results.

    $\displaystyle (a) \sin (90-\theta)^o = \cos \theta^o$
    $\displaystyle (b) \sin (270 + \theta)^o = -\cos \theta^o$
    $\displaystyle (c) \tan (\theta - 180)^o = \tan \theta^o$

    Attempt:
    I don't know how to start
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  2. #2
    Moo
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    Hello,

    For the first one, there are two ways imho :
    - sketch a trigonometrical circle and you will see that this relation is true
    - use the formula sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

    For the second one, use the periodicity :
    - the sine function is 360-periodic. Hence $\displaystyle sin(270+\theta)=sin((270+\theta)-360)=sin(\theta-90)$

    - As the sine function is an odd function, sin(-x)=-sin(x)
    - $\displaystyle sin(\theta-90)=-sin(90-\theta)$ and you retrieve the first relation
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