# PracticeLarger 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.