The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
The trigonometric functions are the trigonometric ratios of a triangle. The trigonometric functions sine, cosine, and tangent, are abbreviated as sin, cos, and tan. Let’s look at how specific ratios or functions are measured in a right-angled triangle.
In a right-angled triangle, the longest side is the hypotenuse, with the adjacent and reverse sides being similar and opposite.
Some trigonometry angles 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees are widely seen in trigonometry issues. These angles’ trigonometric proportions, like sin, cosine, and tangent, are straightforward to remember. To locate certain angles, one must first outline a right-angled triangle within which one significant acute angle corresponds to the trigonometric angle. Those angles will be described in relation to the ratio concerned.
For instance in right-angled triangle,
Sin = Perpendicular/Hypotenuse
i.e. θ = (P/H) = sin-1
In the same way,
θ = (Base/Hypotenuse) = cos-1
θ = (Base/Perpendicular) = tan-1
Complementary angles are the sequence of two angles whose sum equals 90 degrees in mathematics. The angles 30° and 60°, for example, are complementary since their sum is 90°. It is observed in complementary triangles.
If two angles, say X and Y, are complementary, they are considered to be complementary.
X + Y = 90 degrees
X is defined as the counterpart of Y in this situation and vice versa.
Since the right angle calculation is set in a right-angle triangle, the other two angles still shape the complement since the number of angles in a triangle is 180°.
There are many real-world applications of trigonometry.
Suppose we have the building’s height and the angle created when an object is viewed from the top of the building. In that case, we may use the tangent function to find the difference between the object and the building’s bottom. For example, the tan of the angle equals the combination of the building’s height and the distance.
Oceanography, seismology, meteorology, physical sciences, physics, acoustics, mapping, communications, among other areas, have used trigonometry. It may also be used to calculate the height of a peak, the duration of a large river, among other related tasks.
In this chapter, we talked about trigonometry and its concepts in detail. We can solve simple 2D problems involving one right-angled triangle in the curriculum and apply them to real-life concepts with this knowledge.