help help anyone could help to  explain to me how to use sine cosine and tangent clearly????

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello, let me try:)

There are many-many ways to use sine, cosine and tangent. I'll start from the origin — "solving" of right triangles.

Let ABC be the triangle with the right angle B. Denote the measure of the angle BAD as α. Then by the definition

cos(α) = AB/AC
the cathetus (leg) forming this angle (the adjacent one) divided by the hypotenuse

sin(α) = BC/AC
the cathetus (leg) NOT forming this angle (the opposite one) divided by the hypotenuse

tan(α) = BC/AB
the opposite cathetus divided by the adjacent cathetus.

And please note that for given angle the values of cos, sin and tan do NOT depend on the choose of a triangle — for any triangle with the same angle α trigonometric functions will be the same.


Now what this all good for.
There may be a situation when we know or can measure the angle α and some side of a right triangle. Then we can compute two other sides without measuring them.

For example, if we know α and therefore cos(α) and AB then
AC = AB/cos(α).
BC = AB*tan(α).

Imagine that there is a column (pillar) standing right on the ground. And we have measured the distance from some point on the ground to the base of the column. Also we have measured the angle with the help of a protractor. It is also possible that we cannot measure the height of the column directly (cannot climb on it).

But with the formula BC = AB*tan(α) we compute the height.


Also, many processes in nature or society have oscillatory character like sine or cosine or combinations of them (when the domain of these functions is expanded to all real numbers, not only acute angles).

These functions also have many relationships with each other and many beautiful mathematical properties.

If this is not what you want, please ask more specific question within this discussion, I'll try to answer it.

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Nolan McShea | Student

Here is an easy way to remember what sine, cosine, and tangent mean:


The "word" above can be divided into three parts:

  1. SOH - The S can be remembered that it is SINE, the O and the H can remembered that it is opposite/hypotenuse.
  2. CAH - The C can be remembered as COSINE, the A and the H can be remembered as adjacent/hypotenuse.
  3. TOA - The T can be remembered as TANGENT, the O and the A can be remembered as opposite/adjacent. 

Let me draw a picture for you.

The image shows the Sine of A as it equals BC/AC

Hope I helped!

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