Trigonometry formula and identity
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Answer:
Trigonometry is a branch of mathematics that deals with triangles. Trigonometry is also known as the study of relationships between lengths and angles of triangles.
There is an enormous number of uses of trigonometry and its formulae. For example, the technique of triangulation is used in Geography to measure the distance between landmarks; in Astronomy, to measure the distance to nearby stars and also in satellite navigation systems.Below is the table for trigonometry formulas for angles that are commonly used for solving problems.
Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360°
Angles (In Radians) 0° π/6 π/4 π/3 π/2 π 3π/2 2π
sin 0 1/2 1/√2 √3/2 1 0 -1 0
cos 1 √3/2 1/√2 1/2 0 -1 0 1
tan 0 1/√3 1 √3 ∞ 0 ∞ 0
cot ∞ √3 1 1/√3 0 ∞ 0 ∞
csc ∞ 2 √2 2/√3 1 ∞ -1 ∞
sec 1 2/√3 √2 2 ∞ -1 There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, co-secant, tangent and co-tangent.
By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
Reciprocal Identities
The Reciprocal Identities are given as:
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
Step-by-step explanation:
hope it helps
Step-by-step explanation:
Trigonometry formula,
1) sin θ = opposite side/hypotenuse
2) cos θ = adjacent side/hypotenuse
3) tan θ = opposite side/adjacent side
4) cosec θ = 1/sin θ
5) sec θ = 1/cos θ
6) cot θ = 1/tan θ
And Identities,
1) sin² θ + cos² θ = 1
2)sec² θ - tan² θ = 1
3)cosec² θ - cot² θ = 1