SOHCAHTOA
(Trigonometric Ratios)
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). |
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 |
1) In a ΔPQR, ∠Q = 90 ^{0} . Write sin(P), cos(P) and tan(P).
2) In a ΔABC, ∠B=90 ^{0} , 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