This section looks at Sin, Cos và Tan within the field of trigonometry.
Bạn đang xem: Sin cos formula
A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question và the right angle. The opposite side is opposite the angle in question.
In any right angled triangle, for any angle:
The sine of the angle = the length of the opposite side the length of the hypotenuse
The cosine of the angle = the length of the adjacent side the length of the hypotenuse
The tangent of the angle = the length of the opposite side the length of the adjacent side
So in shorthand notation:sin = o/h cos = a/h rã = o/aOften remembered by: soh cah toa
Example
Find the length of side x in the diagram below:
The angle is 60 degrees. We are given the hypotenuse & need to find the adjacent side. This formula which connects these three is:cos(angle) = adjacent / hypotenusetherefore, cos60 = x / 13therefore, x = 13 × cos60 = 6.5therefore the length of side x is 6.5centimet.
This đoạn Clip will explain how the formulas work.
Xem thêm: Check Serial Cho Macbook Chính Hãng Với 3 Cách Kiểm Tra Macbook Air Chính Hãng
The Graphs of Sin, Cos & Tan - (HIGHER TIER)
The following graphs show the value of sinø, cosø và tanø against ø (ø represents an angle). From the sin graph we can see that sinø = 0 when ø = 0 degrees, 180 degrees và 360 degrees.
chú ý that the graph of tung has asymptotes (lines which the graph gets cchiến bại khổng lồ, but never crosses). These are the red lines (they aren"t actually part of the graph).
Also notice that the graphs of sin, cos and tung are periodic. This means that they repeat themselves. Therefore sin(ø) = sin(360 + ø), for example.
Notice also the symmetry of the graphs. For example, cos is symmetrical in the y-axis, which means that cosø = cos(-ø). So, for example, cos(30) = cos(-30).Also, sin x = sin (180 - x) because of the symmetry of sin in the line ø = 90.