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Math Help - Two Trigonometry Problems

  1. #1
    Amy
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    Two Trigonometry Problems

    I have two problems

    1) Express cot 138 15' 10'' as the same function of a positive acute angle and then find its value.


    2) Using exact values find the numerical value of tan 225
    +tan(-45)


    tan(-45) is in 4th quadrant?
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    Quote Originally Posted by Amy View Post
    I have two problems

    1) [B]Express cot 138 15' 10'' as the same function of a positive acute angle and then find its value.
    We can write,

    13815'10''=180 - x
    What is that x ?

    Note, we can write,
    180=17960'=17959'60''
    Thus, we can easily see from this that,
    x=4144'50''

    Now use the identity,
    cot (180-x)=-cot x for x acute.

    Thus,
    cot (13815'10'')=cot(180-4144'50'')=-cot(4144'50'')
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    Quote Originally Posted by Amy View Post
    2) Using exact values find the numerical value of tan 225[/B]+tan(-45)

    Use the identity tan(180+x)=tan x for accute x.

    Thus,
    tan 225=tan(180+45)=tan 45=1.

    For the second tangent, tan(-45), use the identity,
    tan(-x)=-tan x.
    Thus, tan(-45)=-tan(45)=-1.
    Thus,
    1+(-1)=0.

    tan(-45) is in 4th quadrant?
    Yes, just add 360 once and you get,
    360-45=315

    Which is an angle in the 4th quadrant because,
    270<x<360
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