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Trigonometry Function Formulas

Trigonometry Function Formulas

So, here are few Trigonometry Function Formulas. Let’s learn some basics of these formulas.

Trigonometry Function Formulas of a Right Triangle : sin α = a / c = opposite / hypotenuse

cos α =  b / c = adjacent / hypotenuse

tan α = a / b = opposite / adjacent

cot α = b / a = adjacent / opposite

sec α = c / b                       Cosec α = c / a

Basic Formula :

sin2 α + cos2 α = 1

tan α . cot tan α = 1

tan α = sin α / cos α = 1 / cot tan α

cot tan α = cos α / sin α = 1 / tan α

1 + tan2 α = 1 / cos2 α = sec2 α

1 + cot tan2 α = 1 /  sin2 α = cos sec2 α

Trigonometric Table

 α 00 300 450 600 900 1200 1800 2700 3600 sin α 0 1/2 √2/2 √3/2 1 √3/2 0 -1 0 cos α 1 √3/2 √2/2 1/2 0 -1/2 -1 0 1 tan α 0 1/√3 1 √3 ∞ -√3 0 ∞ 0 cot α ∞ √3 1 1/√3 0 -1/√3 ∞ 0 ∞ sec α 1 2/√3 √2 2 ∞ -2 -1 ∞ 1 cosec α ∞ 2 √2 2/√3 1 2/√3 ∞ -1 ∞

Co-Ratios

 sin cos tan cot -α -sin α +cos α -tan α -cot α 900 – α +cos α +sin α +cot α +tan α 900 + α +cos α -sin α -cot α -tan α 1800 – α +sin α -cos α -tan α -cot α 1800 + α -sin α -cos α +tan α +cot α 2700 – α -cos α -sin α +cot α +tan α 2700 + α -cos α +sin α -cot α -tan α 3600k – α -sin α +cos α -tan α -cot α 3600k – α +sin α +cos α +tan α +cot α

• sin(A + B) = sinA cosB + cosA sinB
• sin(A – B) = sinA cosB – cosA sinB

• cos(A + B) = cosA cosB – sinA sinB
• cos(A – B) = cosA cosB + sinA sinB

• tan (A + B) = tanA + tanB / 1 – tanA tanB
• tan(A – B) =  tanA – tanB / 1 + tanA tanB

• cot (A+ B) = cotA cotB – 1 / cotA + cotB

Product of Trigonometric Functions:

• sin α cos β = 1/2 [ sin (α + β) + sin(α – β)]
• cos α sin β = 1/2 [ sin (α + β) – sin(α – β)]
• cos α cos β = 1/2 [ cos (α + β) + cos(α – β)]
• sin α sin β = 1/2 [ cos (α – β) – cos(α + β)]

• tan α tan β = tan α + tan β / cot tan α + cot tanβ = – tanα – tan β / cot tan α – cot tan β

Trigonometric Formula with t = tan(x/2)

sinx = 2t / 1 + t2

cos x = 1 – t2 / 1 + t2

tan x = 2t / 1 – t2

cot x = 1 – t2 / 2t

Trigonometric Relation Between Functions: Angle of a Plane Triangle :

• A, B, C are 3 angles of a triangle
• sin A + sin B + sin c = 4 cos(A / 2) cos(B/2) cos(C/2)
• cosA + cos B + cos C = 4 sin(A/2) sin(B/2) sin(C/2) + 1
• sinA + sinB – sinC = 4sin (A/2) sin (B/2) cos (C/2)

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1. This is good?????

2. Pawan says:

Intellegent

3. Pushpendra says:

Sir me mathematics ka silvers chAiye

4. Neha says:

Please let these formulaes in easy way ..
And don’t expand it so much..

5. sara k r says:

if n is a natural number .which is the solution to the equation tan(5a)=cot(3a)?

a=alpha symbol

6. Brian isayi says:

Nice formulaes

7. bazil bangash says:

i like it……….