Question

all formula trignometry​

Answer 1

Step-by-step explanation:

Trigonometric Ratios

So the general trigonometry ratios for a right-angled triangle can be written as;

sinθ = Opposite

Hypotenuse

cosθ = AdjacentSide

Hypotenuse

tanθ = Oppositeside

AdjacentSide

secθ = Hypotenuse

Adjacentside

cosecθ = Hypotenuse

Oppositeside

cotθ = Adjacentside

Oppositeside

Trigonometric Ratios for Unit Circle

• Similarly, for a unit circle, for which radius is equal to 1, and θ is the angle. The value of hypotenuse and adjacent side here is equal to the radius of the unit circle.

• Hypotenuse = Adjacent side to θ = 1

• Therefore, the ratios of trigonometry are given by:

1. sin θ = y/1 = y
2. cos θ = x/1 = x
3. tan θ = y/x
4. cot θ = x/y
5. sec θ = 1/x
6. cosec θ = 1/y

Trigonometry Identities

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 Angle Formulas

sin(-θ) = -sinθ

cos(-θ) = cosθ

tan(-θ) = -tanθ

cot(-θ) = -cotθ

sec(-θ) = secθ

cosec(-θ) = -cosecθ

Co-function 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

$sin2θ = 2 sinθ cosθ</p><p></p><p>cos2θ = 1 – 2sin2θ</p><p></p><p>tan2θ = 2tanθ1−tan2θ</p><p></p><p>Half Angle Formulas</p><p></p><p>sinθ = ±1−cos2θ2−−−−−−√</p><p></p><p>cosθ = ±1+cos2θ2−−−−−−√</p><p></p><p>tanθ = ±1−cos2θ1+cos2θ−−−−−−√</p><p></p><p>Thrice of Angle Formulas</p><p></p><p>sin3θ = 3sinθ – 4 sin3θ</p><p></p><p>Cos 3θ = 4cos3θ – 3 cosθ</p><p></p><p>Tan 3θ = 3tanθ–tan3θ1−3tan2θ</p><p></p><p>Cot 3θ = cot3θ–3cotθ3cot2θ−1</p><p></p><p>$

$Sum and Difference Formulas</p><p></p><p>Sin (A+B) = Sin A Cos B + Cos A Sin B</p><p></p><p>Sin (A-B) = Sin A Cos B – Cos A Sin B</p><p></p><p>Cos (A+B) = Cos A Cos B – Sin A Sin B</p><p></p><p>Cos (A-B) = Cos A Cos B + Sin A Sin B</p><p></p><p>Tan (A+B) = TanA+TanB1–TanATanB</p><p></p><p>Tan (A-B) = TanA–TanB1+TanATanB</p><p></p><p>Product to Sum Formulas</p><p></p><p>Sin A Sin B = ½ [Cos (A-B) – Cos (A+B)]</p><p></p><p>Cos A Cos B = ½ [Cos (A-B) + Cos (A+B)]</p><p></p><p>Sin A Cos B = ½ [Sin (A+B) + Sin (A-B)]</p><p></p><p>Cos A Sin B = ½ [Sin (A+B) – Sin (A-B)]</p><p></p><p>Sum to Product Formulas</p><p></p><p>Sin A + Sin B = 2 sin A+B2 cos A−B2</p><p></p><p>Sin A – Sin B = 2 cosA+B2 sin A−B2</p><p></p><p>Cos A + Cos B = 2 cosA+B2 cos A−B2</p><p></p><p>Cos A – Cos B = – 2 sinA+B2 sin A−B2</p><p></p><p>Inverse Trigonometric Functions</p><p></p><p>If Sin θ = x, then θ = sin-1 x = arcsin(x)</p><p></p><p>Similarly,</p><p></p><p>θ = cos-1x = arccos(x)</p><p></p><p>θ = tan-1 x = arctan(x)</p><p></p><p>Also, the inverse properties could be defined as;</p><p></p><p>sin-1(sin θ) = θ</p><p></p><p>cos-1(cos θ) = θ</p><p></p><p>tan-1(tan θ) = θ</p><p></p><p>Unit Circle</p><p></p><p>With the help of unit circle, we can see here the different values of sin and cos ratios for different angles such as 0°, 30°, 45°, 60°, 90°, and so on in all the four quadrants.</p><p></p><p>$