trigonometry formulas
Answers
Answer:
the general trigonometry ratios for a right-angled triangle can be written as;
sinθ = OppositesideHypotenuse
cosθ = AdjacentSideHypotenuse
tanθ = OppositesideAdjacentSide
secθ = HypotenuseAdjacentside
cosecθ = HypotenuseOppositeside
cotθ = AdjacentsideOppositeside
Similarly, for a unit circle, for which radius is 1, and θ is the angle.Then,
sinθ = y/1
cosθ = x/1
tanθ = y/x
cotθ = x/y
secθ = 1/x
cosecθ = 1/y
Trigonometry Identities and Formulas
Tangent and Cotangent Identities
tanθ = sinθcosθ
cotθ = cosθsinθ
Reciprocal Identities
sinθ = 1/cosecθ
cosecθ = 1/sinθ
cosθ = 1/secθ
secθ = 1/cosθ
tanθ = 1/cotθ
cotθ = 1/tanθ
Pythagorean Identities
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ
Even and Odd Formulas
sin(-θ) = -sinθ
cos(-θ) = cosθ
tan(-θ) = -tanθ
cot(-θ) = -cotθ
sec(-θ) = secθ
cosec(-θ) = -cosecθ
Cofunction Formulas
sin(900-θ) = cosθ
cos(900-θ) = sinθ
tan(900-θ) = cotθ
cot(900-θ) = tanθ
sec(900-θ) = cosecθ
cosec(900-θ) = secθ
Formulas for twice of angle
sin2θ = 2 sinθ cosθ
cos2θ = 1 – 2sin2θ
tan2θ = 2tanθ1−tan2θ
Half Angle Formulas
sinθ = ±1−cos2θ2−−−−−−√
cosθ = ±1+cos2θ2−−−−−−√
tanθ = ±1−cos2θ1+cos2θ−−−−−−√
Formulas for Thrice of angle
sin3θ = 3sinθ – 4 sin3θ
Cos 3θ = 4cos3θ – 3 cosθ
Tan 3θ = 3tanθ–tan3θ1−3tan2θ
Cot 3θ = cot3θ–3cotθ3cot2θ−1
The Sum and Difference Formulas
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) = TanA+TanB1–TanATanB
Tan (A-B) = TanA–TanB1+TanATanB
The Product to Sum Formulas
Sin A Sin B = ½ [Cos (A-B) – Cos (A+B)]
Cos A Cos B = ½ [Cos (A-B) + Cos (A+B)]
Sin A Cos B = ½ [Sin (A+B) + Sin (A+B)]
Cos A Sin B = ½ [Sin (A+B) – Sin (A-B)]
The Sum to Product Formulas
Sin A + Sin B = 2 sin A+B2 cos A−B2
Sin A – Sin B = 2 cosA+B2 sin A−B2
Cos A + Cos B = 2 cosA+B2 cos A−B2
Cos A – Cos B = – 2 sinA+B2 sin A−B2
Inverse Trigonometric Functions
If Sin θ = x, then θ = sin-1 x = arcsin(x)
Similarly,
θ = cos-1x = arccos(x)
θ = tan-1 x = arctan(x)
Also, the inverse properties could be defined as;
sin-1(sin θ) = θ
cos-1(cos θ) = θ
Step-by-step explanation:
Here the answer regarding your problem.
