# Math Help - Actual formulas for trigonometric functions? (no calculator)

1. ## Actual formulas for trigonometric functions? (no calculator)

Hi,

I need to know the actual formulas for the trigonometric functions: sine, cosine, tangent, arcsine, arccosine, arctangent, etc.

What I need is a function, like that of a calculator, for example cosine, which only takes the radian value of angle and returns a value, just like the calculator, but I need to manually calculate it. Those are formulas/procedures I need but I have never been able to find.

From what I can see, for example Cosine, would take the angle in Radians, and would asume a Radius of 1. Since Cosine of an angle is equals to Rx/R, and since Radius is assumed to be 1 and the angle is known, only Rx would need to be determined (presumably would be the direct value Cosine would return), maybe with Pythagoras, but I can't see how if Pythagoras formulas are supposed to use Sine, Cosine, etc., as well. Then I need that you tell me the actual procedure for manually finding Sine, Cosine, and the rest of functions.

If you can also, provide a rationale as to what the different functions are doing. If you can't provide a very extensive explanation, the formulas alone would suffice and I would try to figure them out myself.

If you can, please tell me also where I can find a full, in-depth analysis of the unit circle, like Pythagoras would relate and develop the different components, with the formulas I asked for above, and why they are being developed a particular way, so I can study further by myself, and any other web resource and/or book I should refer to make sense of this normally canned-only functions.

Any information will be welcome, as I see the need of being able to calculate these trigonometric functions manually, without using the calculator or tools, to greatly and really improve math understanding.

2. Originally Posted by x87
Hi,

I need to know the actual formulas for the trigonometric functions: sine, cosine, tangent, arcsine, arccosine, arctangent, etc.

What I need is a function, like that of a calculator, for example cosine, which only takes the radian value of angle and returns a value, just like the calculator, but I need to manually calculate it. Those are formulas/procedures I need but I have never been able to find.

From what I can see, for example Cosine, would take the angle in Radians, and would asume a Radius of 1. Since Cosine of an angle is equals to Rx/R, and since Radius is assumed to be 1 and the angle is known, only Rx would need to be determined (presumably would be the direct value Cosine would return), maybe with Pythagoras, but I can't see how if Pythagoras formulas are supposed to use Sine, Cosine, etc., as well. Then I need that you tell me the actual procedure for manually finding Sine, Cosine, and the rest of functions.

If you can also, provide a rationale as to what the different functions are doing. If you can't provide a very extensive explanation, the formulas alone would suffice and I would try to figure them out myself.

If you can, please tell me also where I can find a full, in-depth analysis of the unit circle, like Pythagoras would relate and develop the different components, with the formulas I asked for above, and why they are being developed a particular way, so I can study further by myself, and any other web resource and/or book I should refer to make sense of this normally canned-only functions.

Any information will be welcome, as I see the need of being able to calculate these trigonometric functions manually, without using the calculator or tools, to greatly and really improve [your] math understanding.
Unless you have studied power series I don't see how the functions you're asking for can possbly be of any use to "really improve math understanding."