Tangent of angle and (but it is not equal to 90 degrees) is called the relation of a sine and to a cosine and. That is to calculate a tangent, it is required to calculate a sine and a cosine of the angle at first. The tangent is for corners in 0, 30, 45, 60, 90, 180 degrees.
Instruction
1. Value of a tangent for corners of 30 and 60 degrees. Let's consider a triangle of ABC with a right angle of C which has A = 30 degrees, In = 60 degrees. As the leg lying against a corner of 30 degrees is equal to a half of a hypotenuse, BC relation to AB is equal to the relation one to two. So, the sine of 30 degrees is equal 0.5, the cosine of 60 degrees is equal to 0.5 too. Means, the cosine of 30 degrees is equal to the root relation from three to two, and the sine of 60 degrees is equal to the same number.
2. Now through a sine and a cosine we find a tangent of angle: A tangent of 30 degrees = to the relation of a sine of 30 degrees to a cosine of 30 degrees = to the root relation from three to three. The tangent of 60 degrees on the same formula is equal to a root from three.
3. Value of a tangent for a corner in 45 degrees. For this purpose we will consider a triangle with a right angle With and corners And yes In on 45 degrees everyone. In this triangle the EXPERT = VS, a corner And = to a corner In = to 45 degrees. On Pythagorean theorem the EXPERT = VS = to AV relation to a root from two. Therefore, the sine of 45 degrees is equal to the root relation from two to two, the cosine of 45 degrees is equal to the same, and the tangent is equal to unit.
4. Now we will find values of a sine, a cosine and a tangent for corners in 0, 90 and 180 degrees. These values are: Sine of 0 degrees = 0, sine of 90 degrees = 1, sine of 180 degrees = 0. The cosine of 0 degrees = 1, a cosine of 90 degrees is equal 0, the cosine of 180 degrees is equal to-1. Thus, the tangent of 0 degrees is equal 0, the tangent of 180 degrees is equal 0, and the tangent of 90 degrees is not defined since at its stay in a denominator it turns out 0, and expression does not make sense.