## TRIGONOMETRIC FORMULAS

In this section, you will learn different trigonometric formulas.

## SOHCAHTOA

sin θ  =  Opposite side / Hypotenuse side

cos θ  =  Adjacent side / Hypotenuse side

tan θ  =  Opposite side / Adjacent side

csc θ  =  Hypotenuse side / Opposite side

sec θ  =  Hypotenuse side / Adjacent side

cot θ  =  Adjacent side  / Opposite side

## Reciprocal Trigonometric Formulas

sin θ and csc θ are reciprocal to each other

cos θ and sec θ are reciprocal to each other

tan θ and cot θ are reciprocal to each other

Then,

sin θ  =  1 / csc θ  and  csc θ  =  1 / sin θ

cos θ  =  1 / sec θ  and  sec θ  =  1 / cos θ

tan θ  =  1 / cot θ  and  cot θ  =  1 / tan θ

## Other Important Trigonometric Formulas

sin2θ  + cos2θ  =  1

sin2θ  =  1 - cos2θ

cos2θ  =  1 - sin2θ

sec²2θ - tan2θ  =  1

sec2θ  =  1 +  tan2θ

tan2θ  =  sec2θ - 1

cosec2θ - cot2θ  =  1

cosec2θ  =  1 + cot2θ

cot2θ  =  cosec2θ - 1

## Double Angle Formulas

sin 2A  =  2sin A cos A

cos 2A  =  cos2A - sin2A

tan 2A  =  2 tan A / (1 - tan2A)

cos 2A  =  1 - 2sin2A

cos 2A  =  2cos2A - 1

sin 2A  =  2 tan A / (1 + tan2A)

cos 2A  =  (1 - tan2A) / (1 + tan2A)

sin²A  =  (1 - cos 2A) / 2

cos²A  =  (1 + cos 2A) / 2

These identities are applied in both the ways ,left to right and  right to left.

## Half Angle Formulas

sin A  =  2sin (A/2) cos (A/2)

cos A  =  cos2(A/2) - sin2(A/2)

tan A  =  2tan (A/2) / [1 - tan2(A/2)]

cos A  =  1 - 2sin2(A/2)

cos A  =  2cos2(A/2) - 1

sin A  =  2tan (A/2) / [1 + tan2(A/2)]

cos A  =  [1 - tan2(A/2)] / [1 + tan2(A/2)]

sin2(A/2)  =  (1 - cos A) / 2

cos2(A/2)  =  (1 + cos A) / 2

tan2(A/2)  =  (1 - cos A) / (1 + cos A)

## Compound 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)

## Sum to Product Formulas

sin C + sin D  =  2 sin [(C+D)/2] cos [(C-D)/2]

sin C - sin D  =  2 cos [(C+D)/2] Sin [(C-D)/2]

cos C + cos D  =  2 cos [(C+D)/2] Cos [(C-D)/2]

cos C - cos D  =  2 sin [(C+D)/2] Sin [(C-D)/2]

## sin3A cos3A tan3A formulas

sin 3A  =  3 sin A - 4 sin3A

cos 3A  =  4 cos3A - 3 cos A

tan 3A  =  (3 tan A - tan3A) / (1 - 3tan2A)

## Values of Certain Angles ## Solving Word Problems Using Trigonometric Formulas

Step 1 :

Understanding the question and drawing the appropriate diagram are the two most important things to be done in solving word problems in trigonometry.

Step 2 :

If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.

Step 3 :

We have to draw diagram almost for all of the word problems in trigonometry. The diagram we draw for the given information must be correct. Drawing diagram for the given information will give us a clear understanding about the question.

Step 4 :

Once we understand the given information clearly and correct diagram is drawn, solving word problems in trigonometry would not be a challenging work.

Step 5 :

After having drawn the appropriate diagram based on the given information, we have to give name for each position of the diagram using English alphabets (it is clearly shown in the word problem given below). Giving name for the positions would be easier for us to identify the parts  of the diagram.

Step 6 :

Now we have to use the appropriate trigonometric formulas (sin, cos and tan) to find the unknown side or angle.

Once the diagram is drawn and we have translated the English Statement (information) given in the question as mathematical equation using trigonometric ratios correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown. Apart from the stuff given in this section if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 