In this chapter-11 you are going to learn that Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. You have learned about various properties of a right-angled triangle and trigonometric ratios of angles based on sides only.
Table of content in the book:
- Trigonometric Ratios
- Trigonometric Ratios Of Some Specific Angles
- Trigonometric Ratios Of Complementary Angles
- Trigonometric Identities
- Trigonometry solutions
- Conclusion
Trigonometric Ratios
The ratios of sides of a right triangle are known as trigonometric ratios. There are three common trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
- The ratio of the opposite side of an angle and the length of the hypotenuse is constant in all similar right-angle triangles. This ratio is called the “sine” of angle.
- The ratio of adjacent sides of an angle and length of the hypotenuse is constant in all similar right triangles. That ratio is known as the “cosine” of that angle.
- The ratio of the opposite side and the adjacent side of an angle is constant and is called the “tangent” of that angle.
In the right angle triangle, the trigonometric ratios can be defined as follows:
The values of trigonometric ratios of the angles 0°, 30°, 60°, and 90° are given in a table below
Trigonometric Ratios Of Some Specific Angles
Trigonometric Ratios for Complementary Angles
Sin (90° – A) = cos A
Cos (90° – A) = sin A
Tan (90° – A) = cot A
Cot (90° – A) = tan A
Sec (90° – A) = cosec A
Cosec (90° – A) = sec A
Note:
Here (90° – A) is the complementary angle of A.
Trigonometric Identities:
An equation involving the trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.
(i) sec2θ – tan2θ = 1 [for 0° ≤ θ ≤ 90°]
(ii) cosec2θ – cot2θ = 1 [for 0° < θ ≤ 90°]
(iii) sin2θ + cos2θ = 1 [for 0° ≤ θ ≤ 90°]
Trigonometry solutions:
Have the practice of problems which are given below.
There are different methods of problems given below from the different exercises, Rest of the examples given in the book refer to it and all solve the problems which are given.
Conclusion
SO we conclude that without trigonometry, Life would be very much difficult. We are going through without troubles, we can easily find something so we think that it was a good invention by Archimedes and thanks to this many architects need not go through the trouble for calculating the things, so it helps in real-life applications and not only in our tests and exams.