Trigonometry – Class 11 Maths NCERT Solutions
Class 11 Maths: Trigonometry is the branch of mathematics which deals with phenomenon related to height and distance. sine, cosine, and tangent are the basic and main functions of trigonometry.Trigonometry is basically derived from Greek word where trigonon means “triangle” and metron means “measure”.
Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.
Figure showing measurements are considered as sides of right-angled triangle and results can be carried out with the help of identities related to sine, cosine, and tangent of a number.
This article uses Greek letters such as alpha (α), beta (β), gamma (γ), and theta (θ) to represent angles. Several different units of angle measure are widely used, including degrees, radians, and gradians (gons):
1 full circle (turn) = 360 degrees = 2π radians = 400 gons.
Value of sine and cosines around the circles.
The tangent (tan) of an angle is the ratio of the sine to the cosine:
Tan θ = sinθ/cosθ ;
Finally, the reciprocal functions secant (sec), cosecant (csc), and cotangent (cot) are the reciprocals of the cosine, sine, and tangent
sec θ=1/cos θ,cscθ =1/θ,cot θ=1/tan θ=cos θ/sin θ
These definitions are sometimes referred to as ratio identities.
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In trigonometry, the basic relationship between the sine and the cosine is known as the Pythagorean identity:
where cos2 θ means (cos(θ))2 and sin2 θ means (sin(θ))2.
Dividing the Pythagorean identity by either cos2 θ or sin2 θ yields two other identities:
1+tan2θ=sec2θ , 1+cot2θ =cosec2θ;
Using these identities together with the ratio identities, it is possible to express any trigonometric function in terms of any other.
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