Sin (A+B+C) Calculator

✖Sin A is the value of the trigonometric sine function of the angle A.ⓘ Sin A			+10% -10%
✖Cos B is the value of the trigonometric cosine function of the angle B.ⓘ Cos B			+10% -10%
✖Cos C is the value of the trigonometric cosine function of the angle C.ⓘ Cos C			+10% -10%
✖Cos A is the value of the trigonometric cosine function of the angle A.ⓘ Cos A			+10% -10%
✖Sin B is the value of the trigonometric sine function of the angle B.ⓘ Sin B			+10% -10%
✖Sin C is the value of the trigonometric sine function of the angle C.ⓘ Sin C			+10% -10%

✖Sin (A+B+C) is the value of the trigonometric sine function of the sum of three given angles, angle A, angle B and angle C.ⓘ Sin (A+B+C) [sin_(A+B+C)]

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Formula

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Sin (A+B+C)

Formula

`"sin"_{"(A+B+C)"} = ("sin A"*"cos B"*"cos C")+("cos A"*"sin B"*"cos C")+("cos A"*"cos B"*"sin C")-("sin A"*"sin B"*"sin C")`

Example

`"0.685632"=("0.34"*"0.87"*"0.65")+("0.94"*"0.5"*"0.65")+("0.94"*"0.87"*"0.29")-("0.34"*"0.5"*"0.29")`

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Download Product to Sum, Sum to Product, Sum & Difference Trigonometry Identities Formulas PDF PDF Image

Sin (A+B+C) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C)
sin_(A+B+C) = (sin A*cos B*cos C)+(cos A*sin B*cos C)+(cos A*cos B*sin C)-(sin A*sin B*sin C)
This formula uses 7 Variables

Variables Used

Sin (A+B+C) - Sin (A+B+C) is the value of the trigonometric sine function of the sum of three given angles, angle A, angle B and angle C.
Sin A - Sin A is the value of the trigonometric sine function of the angle A.
Cos B - Cos B is the value of the trigonometric cosine function of the angle B.
Cos C - Cos C is the value of the trigonometric cosine function of the angle C.
Cos A - Cos A is the value of the trigonometric cosine function of the angle A.
Sin B - Sin B is the value of the trigonometric sine function of the angle B.
Sin C - Sin C is the value of the trigonometric sine function of the angle C.

STEP 1: Convert Input(s) to Base Unit

Sin A: 0.34 --> No Conversion Required
Cos B: 0.87 --> No Conversion Required
Cos C: 0.65 --> No Conversion Required
Cos A: 0.94 --> No Conversion Required
Sin B: 0.5 --> No Conversion Required
Sin C: 0.29 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

sin_(A+B+C) = (sin A*cos B*cos C)+(cos A*sin B*cos C)+(cos A*cos B*sin C)-(sin A*sin B*sin C) --> (0.34*0.87*0.65)+(0.94*0.5*0.65)+(0.94*0.87*0.29)-(0.34*0.5*0.29)

Evaluating ... ...

sin_(A+B+C) = 0.685632

STEP 3: Convert Result to Output's Unit

0.685632 --> No Conversion Required

FINAL ANSWER

0.685632 <-- Sin (A+B+C)

(Calculation completed in 00.004 seconds)

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Created by Surjojoti Som

Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore

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< 12 Sum & Difference Trigonometry Identities Calculators

Tan (A+B+C)

Go Tan (A+B+C) = (Tan A+Tan B+Tan C-(Tan A*Tan B*Tan C))/(1-(Tan A*Tan B)-(Tan B*Tan C)-(Tan A*Tan C))

Cot (A+B+C)

Go Cot (A+B+C) = ((Cot A*Cot B*Cot C)-Cot A-Cot B-Cot C)/((Cot A*Cot B)+(Cot B*Cot C)+(Cot A*Cot C))

Sin (A+B+C)

Go Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C)

Cos (A+B+C)

Go Cos (A+B+C) = (Cos A*Cos B*Cos C)-(Cos A*Sin B*Sin C)-(Sin A*Cos B*Sin C)-(Sin A*Sin B*Cos C)

Tan (A+B)

Go Tan (A+B) = (Tan A+Tan B)/(1-(Tan A*Tan B))

Tan (A-B)

Go Tan (A-B) = (Tan A-Tan B)/(1+(Tan A*Tan B))

Cot (A-B)

Go Cot (A-B) = ((Cot B*Cot A)+1)/(Cot B-Cot A)

Cot (A+B)

Go Cot (A+B) = ((Cot B*Cot A)-1)/(Cot B+Cot A)

Sin (A+B)

Go Sin (A+B) = (Sin A*Cos B)+(Cos A*Sin B)

Cos (A+B)

Go Cos (A+B) = (Cos A*Cos B)-(Sin A*Sin B)

Sin (A-B)

Go Sin (A-B) = (Sin A*Cos B)-(Cos A*Sin B)

Cos (A-B)

Go Cos (A-B) = (Cos A*Cos B)+(Sin A*Sin B)

Sin (A+B+C) Formula

Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C)
sin_(A+B+C) = (sin A*cos B*cos C)+(cos A*sin B*cos C)+(cos A*cos B*sin C)-(sin A*sin B*sin C)

What is Trigonometry?

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study and describe properties such as lengths, angles, and areas of triangles, as well as the relationships between these properties and the properties of circles and other geometric shapes. Trigonometry is used in many fields, including physics, engineering, and navigation.

How to Calculate Sin (A+B+C)?

Sin (A+B+C) calculator uses Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C) to calculate the Sin (A+B+C), The Sin (A+B+C) formula is defined as the value of the trigonometric sine function of the sum of three given angles, angle A, angle B and angle C. Sin (A+B+C) is denoted by sin_(A+B+C) symbol.

How to calculate Sin (A+B+C) using this online calculator? To use this online calculator for Sin (A+B+C), enter Sin A (sin A), Cos B (cos B), Cos C (cos C), Cos A (cos A), Sin B (sin B) & Sin C (sin C) and hit the calculate button. Here is how the Sin (A+B+C) calculation can be explained with given input values -> 0.685632 = (0.34*0.87*0.65)+(0.94*0.5*0.65)+(0.94*0.87*0.29)-(0.34*0.5*0.29).

FAQ

What is Sin (A+B+C)?

The Sin (A+B+C) formula is defined as the value of the trigonometric sine function of the sum of three given angles, angle A, angle B and angle C and is represented as sin_(A+B+C) = (sin A*cos B*cos C)+(cos A*sin B*cos C)+(cos A*cos B*sin C)-(sin A*sin B*sin C) or Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C). Sin A is the value of the trigonometric sine function of the angle A, Cos B is the value of the trigonometric cosine function of the angle B, Cos C is the value of the trigonometric cosine function of the angle C, Cos A is the value of the trigonometric cosine function of the angle A, Sin B is the value of the trigonometric sine function of the angle B & Sin C is the value of the trigonometric sine function of the angle C.

How to calculate Sin (A+B+C)?

The Sin (A+B+C) formula is defined as the value of the trigonometric sine function of the sum of three given angles, angle A, angle B and angle C is calculated using Sin (A+B+C) = (Sin A*Cos B*Cos C)+(Cos A*Sin B*Cos C)+(Cos A*Cos B*Sin C)-(Sin A*Sin B*Sin C). To calculate Sin (A+B+C), you need Sin A (sin A), Cos B (cos B), Cos C (cos C), Cos A (cos A), Sin B (sin B) & Sin C (sin C). With our tool, you need to enter the respective value for Sin A, Cos B, Cos C, Cos A, Sin B & Sin C and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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