SOHCAHTOA
(Trigonometric Ratios)

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Trigonometric Ratios (SOHCAHTOA ) :

The word Trigonometry is derived from three Greek words: "Trio" meaning thrice(3), "gonia" meaning measure. Thus , Trigonometry is the study of a three-sided figure i.e. a triangle.
Hipparchus a Greek mathematician, relationships however large or or small measure. The three most used ratio to solve a right angled triangle are the Sine(sin), Cosine(cos) and the Tangent(tan).
The most important task of trigonometry is to find the remaining sides and angles of a triangle when some of its sides and angles are given. This problem is solved by using some ratios of the sides of a triangle with respect to its acute angles. These ratios of acute angles are called Trigonometry ratios of angles.

Let ΔABC, the side opposite to ∠A is ‘a’ , side opposite to ∠B is ‘b’ and side opposite to ∠C is ‘c’.

In a right angled triangle, 1) Adjacent side(A) is adjacent to the angle "θ” 2) Opposite side(O) is opposite the angle “θ", 3) the longest side is the Hypotenuse (H).

We define the following six trigonometric ratios.

SOH-CAH-TOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e.,

1) Sine Function: Sinθ= Opposite/ Hypotenuse = O/H (SOH) 2)Cosine Function : Cosθ = Adjacent / Hypotenuse =A/H (CAH) 3)Tangent Function : tanθ = Opposite / Adjacent = O/A (TOA) 4) Cosecant Function : cosecθ = Hypotenuse / Opposite = H/O 5)Secant Function: Secθ = Hypotenuse /Adjacent = H/A 6) Cotangent Function : Cotθ = Adjacent / Opposite = A/ H

Practice
1) In a ΔPQR, ∠Q = 90⁰. Write sin(P), cos(P) and tan(P).
2) In a ΔABC, ∠B=90⁰, AB= 6, BC= 8 find sin(c),cos(C), tan(c), csc(C), sec(C) and cot(C).
3) In ΔMNO, tan(M)= 5/12, find sin(M) and cos(M).

---

Trigonometry

• SOHCAHTOA -Introduction to Trigonometry
• Trigonometric ratios and their Relation
• Trigonometry for specific angles
• Complementary angles in Trigonometry
• Trigonometric Equations

Home Page

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.