Math - Sine, Cosine, and Tangent - Pt1

In this lecture we looked at the relationships that exist between the sine, cosine, and tangent on the unit circle and looked at how they change for different angles.

In the next lecture we’ll be expanding on this even further, so stay tuned for part 2!

Another way to see why tangent becomes undefined at 90 and 270 degrees, is not only because we can’t divide by zero, but also because it becomes parallel to the x-axis (as parallels never meet).

Hi. I don’t understand the Tangent. In the video it is explained that it extends at a right angle until it touches the x-axis. What right angle are you referring to? The one between the sin and the x-axis? I understand the relationship between Sin and Cos and why the simulation behaves that way as you change the degrees, but I can’t grasp why the tangent behaves that way.

For example why does it behave like this?

And not like this which would give us a different Tangent value?

Great question @Alejandro_Borge1.
The tangent extends at a right-angle to the radial line (in green).


Give the animation another watch with that in mind it should hopefully make a bit more sense, but if you’re still struggling then please let me know.

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This clears everything up. Thanks.

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Bit of question and confirmation here: So, would it be incorrect to say that the tan(1) = infinity (in general this is how I remember being taught divisions by zero, though I could certainly see the case either way looking at things graphically given an infinite amount of distance or time is effectively the same as saying never reaching)?

Hi,

Tan (90) = undefined actually; sin(90 = 1 and cos(90) = 0. You can also explain tangent of an angle is by dividing opposite line by the neighbor line. So in this “right angle” case your neighbor line is simply equal to 0 and the opposite line is 1.

Thinking back then I almost failed 1 year in the high school 23 years ago because of trigonometry and now explaining things here…

P.S: any number / 0 is equal to; If you are physicist, it can be zero depending on the theory you are applying it. However, if you are a mathematician, it is undefined.

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Thanks for that. I won’t claim to be a mathematician - it stopped clicking for me somewhere around proofs in university (honestly I don’t know how I passed some of the courses I took, coupled with a few close shaves :laughing:) and most of that’s been forgotten with the sands of time.

Honestly, I can’t quite remember where i got the idea for infinity either, though I thought it was some professor or other along the way.

kek =)) You might have mixed it up with the result of sin 90. A tired mind can trick person very very easily. And it seems the summer lectures back then worked on me…