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Q: Why is it tangent 90 degrees is undefined?

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It is 90 degrees between the circle's diameter and its tangent

The tangent of 75 degrees is: 3.7320507852401

Tangent is 0.5317

90 degrees. QED.

Although you haven't expressed it too clearly in your question, I think what you may belooking for is the angle whose tangent is 4,900, and the angle whose tangent is 19,600 .The problem is that the tangent of 89 degrees is about 57.3, and every numberfrom 57.3 all the way up to 'infinity' is the tangent of an angle somewhere in thatlast degree, between 89 and 90 . . . They really bunch up in there !4,900 is the tangent of 89.9883 degrees. (rounded)19,600 is the tangent of 89.9971 degrees. (rounded)

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tan(x) = sin(x) /cos(x).When x = 90 degrees then cos(x) = 0 so tan(x) requires division by zero - which is not defined.

90 degrees is one

Everytime you determine on your calculators the tangent of 90 degrees, it returns an electron overflow equivalent to a machine-shriek. This is due to the fact that the formula attempted to divide by zero, thus, the result of TANGENT of 90 degrees is UNDEFINED(Division By ZERO is UNDEFINED/not allowed). All lines following this formula is parallel to the y-axis, including the line on the y-axis itself. Hence, point of tangency is impossible to define since parallel lines NEVER MEET.

The angle between the radius and the tangent is a right angle of 90 degrees.

It is 90 degrees between the circle's diameter and its tangent

-pi/2 and pi/2

It's not. The tangent of 180 degrees is zero. Consider tan(x) = sin(x)/cos(x). When x = 180 degrees, sin(x) = 0 and cos(x) = -1 and so tan(x) = 0

Just as at 90 degrees, it goes to infinity. That is because tangent of angle is opposite side over adjacent side. The oppsoite side gets bigger and bigger after 45 dgerees ( and in your case then after 225 degrees) until it grows beyond all bounds at 270 degrees

the tangent of 60 degrees is 1.7321

The tangent of 75 degrees is: 3.7320507852401

Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.

The tangent of 89 degrees is: 57.3

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