Verify Trigonometric Identities - G...
Verify Trigonometric Identities - Grade 12

(Trigonometric Ratios)

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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


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).

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

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