Trignometry

Values Of Trigonometric Ratios

Introduction to trigonometryThe word trigonometry is derived from the Greek words tri (meaning three), gon (meaning sides ) and metron (meaning measure). In fact, Trigonometry is the study of the relationships between the sides and angles of a triangle. Trigonometric ratios of an angle are some ratios of the sides of a right triangle with respect to its acute angles. Trigonometric identities are some trigonometric ratios for some specific angles and some identities involving these ratios.Next SlidePrevious Slide

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Welcome to the world of trigonometryNext SlidePrevious Slide

HOMECosine of angle BTangentSineClearAB90oCacbcos(B) ==accos(A)adjacenthypotenuseNext SlidePrevious SlideHOMETrigonometric ratiosLet us take a right angle ABC as shown in figure.Here, ACB or C is an acute angle. Note the position of side AB with respect to C. It faces C. we call it the side opposite to C(perpendicular). AC is hypotenuse of the right angle and the side BC is a part of C. so, we call it the side adjacent to C(base).

Next SlidePrevious SlideHOMEnames of trigonometric ratiosNAMESWRITTEN ASSine Sin Cosine Cos Tangent Tan Cosecant Cosec Secant Sec Cotangent Cot Next SlidePrevious Slide

HOMETrigometric ratiosDefinitions of sine cosine & tangent

adjacent sideopposite sideanglehypotenuseNext SlidePrevious SlideHOMETriangle terminologyOpposite sideAdjacent sideHypotenuseNext SlidePrevious SlideHOMEquestions related to above topicsCalculating the value of other trigonometric ratios, if one is given.Proving type.Evaluating by using the given trigonometric ratios value.Next SlidePrevious Slide

HOMEType 1 calculating value of other trigonometric ratios, if one is given.If Sin A = 3 / 4 , calculate Cos A and Tan A .Solution - Sin A = P / H = BC / AC = 3 / 4 Let BC = 3KAND , AC = 4K THEREFORE, By Pythagoras Theorem, (AB) = (AC) (BC) (AB) = (4K) - (3K) AB = 7K Cos A = B / H= AB / AC = 7K / 4K = 7 / 4 Tan A = P / B = BC / AB = 3K / 7K = 3 / 7

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HOMEType 2 proving typeIf A and B are acute angles such that Cos A = Cos B, then show that A = B Solution - Since, Cos A = Cos B AC / AB = BC / AB therefore, AC = BC. B = A (angles opposite to equal sides ) Therefore , A = B

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HOMEType 3 evaluating by putting the given trigonometric ratios value If Sec A = 5 / 4 , evaluate 1 Tan A . 1 + Tan ASolution Sec A = H / B =AC / AB = 5 / 4Let AC / AB = 5K / 4K. By Pythagoras Theorem , (BC) = (AC ) (AB) Therefore, BC = 3KSo, Tan A = P / B = BC / AB = 3K / 4K = 3 / 4 1 Tan A = 1 3 / 4 = 1 / 4 = 1 1 + Tan A 1 + 3 / 4 7 / 4 7

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HOMEValues Of Trigonometric Ratios 030456090Sin 01/21/23/21Cos 13/21/21/20Tan 01/313NOTDEFINEDCosec NOTDEFINED222/31Sec 12/322NOT DEFINEDCot NOT DEFINED311/30Next SlidePrevious Slide

HOME examples ON VALUES OF TRIGONOMETRIC RATIOSEvaluationFinding values of A and B.

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HOMEType 1 - evaluationSin 60 * cos 30 + sin 30 * cos60 =3 / 2 * 3 / 2 + 1 / 2 * 1 / 2 = 3 / 4 + 1 / 4 = 4 / 4 = 1Next SlidePrevious Slide

HOMEType 2 finding values of a and bIf Tan (A+B) = 3 and tan ( A B) = 1/ 3 ; 0 < A + B 90 ; A> B , find A and B. Solution tan (A + B ) = 3 tan (A+ B ) = tan 60 A+ B = 60 - ( 1) tan (A- B) = 1 / 3 tan (A- B) = tan 30 A B = 30 - ( 2 ) From ( 1 ) & ( 2) A = 45 B = 15 Next SlidePrevious Slide

HOMEFORMULASSin ( 90 ) = Cos Cos ( 90 ) = Sin

Tan ( 90 ) = Cot Cot ( 90 ) = Tan

Cosec ( 90 ) = Sec Sec ( 90 ) = Cosec Next SlidePrevious Slide

HOMEExample on formulasEvaluate : -(1) Sin 18 / Cos 72 = Sin (90 72 ) / Cos 72 = Cos 72 / Cos 72 = 1( 2) Cos 48 Sin 42 = Cos ( 90 42 ) Sin 42 = Sin 42 Sin 42 = 0Next SlidePrevious Slide

HOMEMain identities Sin + Cos = 11 + Tan = Sec 1 + Cot = Cosec Sin / Cos = Tan Cos / Sin = Cot Sin / Cos = Tan Cos / Sin = Cot Next SlidePrevious Slide

HOMESteps of proving the identitiesSolve the left hand side or right hand side of the identity.Use an identity if required.Use formulas if required.Convert the terms in the form of sin or cos according to the question.Divide or multiply the L.H.S. by sin or cos if required.Then solve the R.H.S. if required.Lastly , verify that if L.H.S. = R.H.S.Next SlidePrevious Slide

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THE ENDPROJECT MADE BY SHUBHAM KUMARPrevious Slide

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