Basic trigonometric formula…
The trigonometric formulas for ratios are majorly based on the three sides of a right-angled triangle, such as the adjacent side or base, perpendicular and hypotenuse . Applying Pythagoras theorem for the given right-angled triangle, we have: following formula are sufficient for class 10 student..
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (P)2 + (B)2 = (H)2
Now, let us see the formulas based on trigonometric ratios (sine, cosine, tangent, secant, cosecant and cotangent)
Basic Trigonometric formulas
The Trigonometric formulas are given below: You Can use the formula
S.no A.Property Mathematical value
1 sin A Perpendicular/Hypotenuse
2 cos A Base/Hypotenuse
3 tan A Perpendicular/Base
4 cot A Base/Perpendicular
5 cosec A Hypotenuse/Perpendicular
6 sec A Hypotenuse/Base
Reciprocal Relation Between Trigonometric Ratios
S.no.B. Identity Relation
1 tan A sin A/cos A
2 cot A cos A/sin A
3 cosec A 1/sin A
4 sec A 1/cos A
Trigonometric Sign Functions
sin (-θ) = − sin θ
cos (−θ) = cos θ
tan (−θ) = − tan θ
cosec (−θ) = − cosec θ
sec (−θ) = sec θ
cot (−θ) = − cot θ
Trigonometric Identities
sin2A + cos2A = 1
tan2A + 1 = sec2A
cot2A + 1 = cosec2A
Periodic Identities
sin(2nπ + θ ) = sin θ
cos(2nπ + θ ) = cos θ
tan(2nπ + θ ) = tan θ
cot(2nπ + θ ) = cot θ
sec(2nπ + θ ) = sec θ
cosec(2nπ + θ ) = cosec θ
Complementary Ratios
Quadrant I
sin(π/2 − θ) = cos θ
cos(π/2 − θ) = sin θ
tan(π/2 − θ) = cot θ
cot(π/2 − θ) = tan θ
sec(π/2 − θ) = cosec θ
cosec(π/2 − θ) = sec θ
Quadrant II
sin(π − θ) = sin θ
cos(π − θ) = -cos θ
tan(π − θ) = -tan θ
cot(π − θ) = – cot θ
sec(π − θ) = -sec θ
cosec(π − θ) = cosec θ
Quadrant III
sin(π + θ) = – sin θ
cos(π + θ) = – cos θ
tan(π + θ) = tan θ
cot(π + θ) = cot θ
sec(π + θ) = -sec θ
cosec(π + θ) = -cosec θ
Quadrant IV
sin(2π − θ) = – sin θ
cos(2π − θ) = cos θ
tan(2π − θ) = – tan θ
cot(2π − θ) = – cot θ
sec(2π − θ) = sec θ
cosec(2π − θ) = -cosec θ
Sum and Difference of Two Angles
sin (A + B) = sin A cos B + cos A sin B
sin (A − B) = sin A cos B – cos A sin B
cos (A + B) = cos A cos B – sin A sin B
cos (A – B) = cos A cos B + sin A sin B
tan(A + B) = [(tan A + tan B)/(1 – tan A tan B)]
tan(A – B) = [(tan A – tan B)/(1 + tan A tan B)]
Double Angle Formulas
sin 2A = 2 sin A cos A = [2 tan A /(1 + tan2A)]
cos 2A = cos2A – sin2A = 1 – 2 sin2A = 2 cos2A – 1 = [(1 – tan2A)/(1 + tan2A)]
tan 2A = (2 tan A)/(1 – tan2A)
Triple Angle Formulas.
sin 3A = 3 sinA – 4 sin3A
cos 3A = 4 cos3A – 3 cos A
tan 3A = [3 tan A – tan3A]/[1 − 3 tan2A
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