Page 1 Trigonometry And its Application Page 2 Trigonometry And its Application Trigonometric Identities similarly sin ? = cosec ? 1 cosec ? = sin ? 1 similarly cos ? = sec ? 1 sec ? = cos ? 1 Complementary Angles sin ? = cos (90 - ? ) cosec ? = sec (90 - ? ) cos ? = sin (90 - ? ) sec ? = cosec (90 - ? ) similarly similarly similarly tan ? = cot (90 - ? ) cot ? = tan (90 - ? ) similarly tan ? = cot ? 1 cot ? = tan ? 1 sin 2 ? + cos 2 ? = 1 cosec 2 ? - cot 2 ? = 1 sec 2 ? - tan 2 ? = 1 Trigonometric Ratios Opposite Hypotenuse sin ? = Opposite Hypotenuse cosec ? = Adjacent Opposite cot ? = Adjacent Hypotenuse sec ? = Adjacent Opposite tan ? = Adjacent Hypotenuse cos ? = Hypotenuse Adj b a c Opp Adj 30 o 60 o 90 o Opp Useful Terms for Application of Trigonometry Angle of elevation (Line of sight) Ground Angle of depression Horizontal line (Parallel to ground) Ground (90 -?) ? ? ? (90 -?) Opposite Hypotenuse Sin = SOH CAH TOA Adjacent Hypotenuse Cos = Adjacent Opposite Tan = TRIGONOMETRY & ITS APPLICATIONS 22 Trigonometry & its Applications Page 3 Trigonometry And its Application Trigonometric Identities similarly sin ? = cosec ? 1 cosec ? = sin ? 1 similarly cos ? = sec ? 1 sec ? = cos ? 1 Complementary Angles sin ? = cos (90 - ? ) cosec ? = sec (90 - ? ) cos ? = sin (90 - ? ) sec ? = cosec (90 - ? ) similarly similarly similarly tan ? = cot (90 - ? ) cot ? = tan (90 - ? ) similarly tan ? = cot ? 1 cot ? = tan ? 1 sin 2 ? + cos 2 ? = 1 cosec 2 ? - cot 2 ? = 1 sec 2 ? - tan 2 ? = 1 Trigonometric Ratios Opposite Hypotenuse sin ? = Opposite Hypotenuse cosec ? = Adjacent Opposite cot ? = Adjacent Hypotenuse sec ? = Adjacent Opposite tan ? = Adjacent Hypotenuse cos ? = Hypotenuse Adj b a c Opp Adj 30 o 60 o 90 o Opp Useful Terms for Application of Trigonometry Angle of elevation (Line of sight) Ground Angle of depression Horizontal line (Parallel to ground) Ground (90 -?) ? ? ? (90 -?) Opposite Hypotenuse Sin = SOH CAH TOA Adjacent Hypotenuse Cos = Adjacent Opposite Tan = TRIGONOMETRY & ITS APPLICATIONS 22 Trigonometry & its Applications Trick To Remember Trigonometry Value Table Step 1 : Write numbers 0-4 Divide them by 4 Take square root 0 1 2 3 4 0 1 2 3 4 4 4 4 4 4 Step 2 : Step 3 : Now we have the values for sin ? Step 4 : Reverse the values of sin ? to obtain the values for cos ? as given in table. Now cosec ? is inverse of sin ? & sec ? is inverse of cos ?, so the values. Similarly value for tan ? & cot ? can be obtained by using Step 5 : Step 6 : 0 0 1 2 3 4 4 4 4 4 4 1 2 1 3 2 1 2 cos ? sin ? sin ? cos ? , cot ? = tan ? = 45 o 60 o 90 o 0 o sin ? ? Ratio cos ? cosec ? sec ? tan ? cot ? 30 o 1 1 1 1 1 1 2 Not Dened Not Dened Not Dened Not Dened 0 0 0 0 1 2 1 2 2 3 2 3 1 3 2 2 2 3 3 3 3 2 3 2 1 2 1 2 sin ? (0 o , 30 o , 45 o , 60 o , 90 o ) TRIGONOMETRY & ITS APPLICATIONS 23 Page 4 Trigonometry And its Application Trigonometric Identities similarly sin ? = cosec ? 1 cosec ? = sin ? 1 similarly cos ? = sec ? 1 sec ? = cos ? 1 Complementary Angles sin ? = cos (90 - ? ) cosec ? = sec (90 - ? ) cos ? = sin (90 - ? ) sec ? = cosec (90 - ? ) similarly similarly similarly tan ? = cot (90 - ? ) cot ? = tan (90 - ? ) similarly tan ? = cot ? 1 cot ? = tan ? 1 sin 2 ? + cos 2 ? = 1 cosec 2 ? - cot 2 ? = 1 sec 2 ? - tan 2 ? = 1 Trigonometric Ratios Opposite Hypotenuse sin ? = Opposite Hypotenuse cosec ? = Adjacent Opposite cot ? = Adjacent Hypotenuse sec ? = Adjacent Opposite tan ? = Adjacent Hypotenuse cos ? = Hypotenuse Adj b a c Opp Adj 30 o 60 o 90 o Opp Useful Terms for Application of Trigonometry Angle of elevation (Line of sight) Ground Angle of depression Horizontal line (Parallel to ground) Ground (90 -?) ? ? ? (90 -?) Opposite Hypotenuse Sin = SOH CAH TOA Adjacent Hypotenuse Cos = Adjacent Opposite Tan = TRIGONOMETRY & ITS APPLICATIONS 22 Trigonometry & its Applications Trick To Remember Trigonometry Value Table Step 1 : Write numbers 0-4 Divide them by 4 Take square root 0 1 2 3 4 0 1 2 3 4 4 4 4 4 4 Step 2 : Step 3 : Now we have the values for sin ? Step 4 : Reverse the values of sin ? to obtain the values for cos ? as given in table. Now cosec ? is inverse of sin ? & sec ? is inverse of cos ?, so the values. Similarly value for tan ? & cot ? can be obtained by using Step 5 : Step 6 : 0 0 1 2 3 4 4 4 4 4 4 1 2 1 3 2 1 2 cos ? sin ? sin ? cos ? , cot ? = tan ? = 45 o 60 o 90 o 0 o sin ? ? Ratio cos ? cosec ? sec ? tan ? cot ? 30 o 1 1 1 1 1 1 2 Not Dened Not Dened Not Dened Not Dened 0 0 0 0 1 2 1 2 2 3 2 3 1 3 2 2 2 3 3 3 3 2 3 2 1 2 1 2 sin ? (0 o , 30 o , 45 o , 60 o , 90 o ) TRIGONOMETRY & ITS APPLICATIONS 23 TRIGONOMETRY & ITS APPLICATIONS 24 Convert all sec, cosec, cot, and tan into sin and cos, Most of this can be done using the quotient and reciprocal identities. Expand the equation if you can, combine like terms, and simplify the equations. Check for angle multiples and remove them using the appropriate Just remember the Sin ? Value in trigonometry value table. Others can be derived easily. For word problem: make proper diagrams by maintaining the aspect ratio of the angles and sides. Also, don’t get confused between angle of elevation and depression (most common mistake). For questions given in the radical form (Square root), try to rationalize it by multiplying the term in the numerator and in the denominator. Just remember one identity Sin 2 ? + Cos 2 ? = 1. We can derive the other identities by just dividing this identity by Sin 2 ? & Cos 2 ? respectively. While solving problems where you have to prove L.H.S = R.H.S, try to bring both the sides to the form of Sin ? and Cos ?. Last but not the least, please remember all the formulae. PLEASE KEEP IN MIND Introduction & Trigonometry Ratios Amazing trick to understand trigonometry formula Scan the QR Codes to watch our free videos Application of trigonometry Simple Trick to remember trigonometry value table How to make clinometer How to use clinometer Board Questions Solved ? ? ? ? ? ? ? ? Speed = Time , Use this formula in problems related to speed and distance. Distance ? ? formulas.Read More

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