cosq = 5/12 and tanq is negative, find the exact value for cscq.
5/12 is a positive number and the cosine is positive in I and IV,
the tangent is negative in II and IV. So, q can only be in IV.
Draw a picture |
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| x
-------|---------
|\ |
| \ |y
| r\ |
| \|
Since cosq = 5/12 = x/r, put 5 for the x and 12 for the r
Draw a picture |
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| 5
-------|---------
|\ |
| \ |y
|12\ |
| \|
Use the Pythagorean theorem
x² + y² = r²
5² + y² = 12²
25 + y² = 144
y² = 119
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y = ±Ö119
Since y goes down, we select the negative sign.
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y = -Ö119
You are asked to find the cscq.
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cscq = r/y = 12/(-Ö119) = -12/Ö119
Edwin
AnlytcPhil@aol.com
