SIN COS TAN Buttons on Calculator - What do they do?

For example If I put tan(4) into a calculator then what am I actually asking the calculator to do? I know tan is short for tangent and tangent is a way of referring to the y/x function but the actual button of the calculator is a mystery to me.

Someone help me understand please.

Depends on degrees or radians. For degrees, it is for a 4 degree angle. For radians, it is for the angle corresponding to the arc that is 4 radians long, assuming the radius is 1 radian long.

Press the tan key, then enter 45, then press the = key.  If the answer is 1 then the  calculator is working in degrees.

Okay, input is angle size and output is function expressed as a decimal. That is what I thought it was but I was getting weird results so I assumed I was wrong about that. I think now the reason I was getting weird results was because I did not know some calculators expect the input to be measured in radians.

Your answers have cleared things up, thanks.

So with Trigonometry the biggest idea revolves around the unit circle and the relation between two measures of angles: Radians and Degrees.

Degrees are quite intuitive. A circle contains 360 degrees. If you divide it in 4 equal quarters than each arc/angle is 90 degrees.

With radians it takes a little bit more thought. What is another way describe the perimeter of a circle? Circumference = 2*pi*radius. Dividing both sides by radius we get Circumference/Radius = 2*pi. By definition, a radian is the arc length of the radius of the circle. Lets do an example: 

If I have a circle with a radius of 4 meters. And arc (part of the circumference) with a length of 4 meters is equal to one radian. Now I’m sure you’re thinking how many radians would there be in the entire circle cause after all we want a part to a whole like 90 degrees to 360 degrees. 

The answer is  2*pi radians because a radian is literally the radius. Essentially an angle of 2*pi radians is equal to an angle of 360 degrees. Same principle works with quarters. Divide 360 by 4 and you get 90 degrees. Divide 2*pi radians by 4 and get pi/2 radians. Pi/2 radians = 90 degrees.

Now with that in mind let’s go to the calculator. You can change the mode in your calculator from Radian to Degrees and vice versa. If you are in degrees, you can type in sin(90) and it will come out to 1 based on the unit circle. But if you’re in radians, the way to get 1 as an output is to type in sin(pi/2).

So when you’re typing in tan(4) in your calculator in Radians mode you’re just saying give me the the ratio of the length opposite to and angle of 4 radians and the length adjacent to the angle of 4 radians of a right triangle in a circle with a radius of 1.

If you were in degree mode you’d be saying the same thing, just the angle would be 4 degrees which is not equivalent to 4 radians.

Let me know if you’re still confused.

Using TAN as an example, the tan button calculates the tan of an angle. 

The tan of the angle is the ratio between O/A.

Conversely, There’s normally also an inverse button you can press before TAN that lets you convert from a ratio to its corresponding angle 

Nope, I got it now. Basically I was assuming the input was in degrees so I would put something like sin(90) expecting the output to be 1 but it was something screwy because unbeknownst to me the calculator took the input as an angle measured in radians.

Very common mistake. Screwed over a lot of people in Pre-Cal and Cal lol

Tangent, sine, cosine... How about you sine your check for my college tuition

Depending on who that is, they might need a cosine. But that's a tangent. Logarithm, anyone?