Question 872173: How do I find the trigonometric function and the requested value?
1. Write the trigonometric function in terms of x
A) cos 0 if tan 0 = x and 0 are in quadrant II
2. Find the requested value
A) Find cot 0 if sec 0 = 25/7 and csc 0 = -25/24
B) Find cot 0 if tan 0 = square root 7/3 and 0 is in quadrant III
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Comment:: trig functions involve opposite, adjacent, and hypotenuse
Since hypo^2 = opp^2 + adj^2, you can find all three value if you
are given 2 of them. And each given trig function gives you 2.
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1. Write the trigonometric function in terms of x
A) cos(t) if tan(t) = x and t is in in quadrant II where opp is positive
and adjacent is negative.
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Since tan = x/1, opp = x and adj = -1
Then hypo = sqrt[x^2+1]
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Therefore: cos = adj/hypo = -1/sqrt(x^2+1)
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2. Find the requested value
A) Find cot 0 if sec 0 = 25/7 and csc 0 = -25/24
If sec is positive and csc is negative, the angle is in QIV
where opp is neg and adj is pos.
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Since sec = 25/7, hypo = 25 and adj = 7
So opp = -sqrt[25^2-7^2] = -sqrt(24)
Therefore cot = adj/opp = -7/sqrt(24)
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B) Find cot 0 if tan 0 = square root 7/3 and 0 is in quadrant III
QIII has adj and opp both negative
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Since tan = 1/cot, tan = 3/sqrt(7)
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Cheers,
Stan H.
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