Practice Larger Trig Quantity 2

puremath

New member
Determine which quantity is larger without a calculator and then use the calculator to check your answer.

(tan 4)(tan 5) or (tan 5)(tan 6)
 

MarkFL

La Villa Strangiato
Math Helper
I'm going to assume the arguments are in degrees, and so we need only consider that on the interval [MATH][0^{\circ},90^{\circ})[/MATH] the tangent function is non-negative and increasing. As both products have [MATH]\tan(5^{\circ})[/MATH] as a factor, we need only consider that we must have:

[MATH]\tan(4^{\circ})<\tan(6^{\circ})[/MATH]
Which then means we must have:

[MATH]\tan(4^{\circ})\tan(5^{\circ})<\tan(5^{\circ})\tan(6^{\circ})[/MATH]
 

puremath

New member
I'm going to assume the arguments are in degrees, and so we need only consider that on the interval [MATH][0^{\circ},90^{\circ})[/MATH] the tangent function is non-negative and increasing. As both products have [MATH]\tan(5^{\circ})[/MATH] as a factor, we need only consider that we must have:

[MATH]\tan(4^{\circ})<\tan(6^{\circ})[/MATH]
Which then means we must have:

[MATH]\tan(4^{\circ})\tan(5^{\circ})<\tan(5^{\circ})\tan(6^{\circ})[/MATH]

1. Cohen did not enclose the arguments in parentheses.

2. There is a picture to be used with this question(s).

3. In terms of radians or degrees, I have to check the textbook again.
 
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