Which trigonometric function has a range that does not include 0.6?
y = cos x
y = sec x
y = tan x
AAAaannndd the bot gets it wrong yet again!
clearly, since |secx| >= 1, the range does not include 0.6
the range of tanx is (-∞,∞)
The trigonometric function that has a range that does not include 0.6 is y = sec x.
To determine which trigonometric function has a range that does not include 0.6, we need to examine the range of each function.
1. y = cos x:
Cosine (cos) is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse of a right triangle. The range of the cosine function is typically between -1 and 1. So, it does include 0.6 as it falls within this range.
2. y = sec x:
Secant (sec) is the reciprocal function of cosine. It is calculated as 1/cos x. The reciprocal of a value does not change the range, so the range of the secant function will also be between -1 and 1. Therefore, it does include 0.6.
3. y = tan x:
Tangent (tan) is the ratio of the opposite side to the adjacent side of a right triangle. The range of the tangent function is from negative infinity to positive infinity, except for certain "undefined" points where the denominator (the adjacent side) equals zero (for any value of x where cos x = 0). Since 0.6 is a real number, it is located within the range of tan x.
Therefore, the function that does not include 0.6 in its range is not listed among the options provided.
The correct answer is y = tan x.
The range of the tangent function is all real numbers except for values of the form (2n + 1)π/2, where n is an integer. In particular, the range of tan(x) does not include 0.6.