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Complementary angles in TrigonometryCovid-19 has led the world to go through a phenomenal transition . E-learning is the future today. Stay Home , Stay Safe and keep learning!!! Complementary angles in trigonometry : Two angles are said to be complementary, if their sum is 90 0 .It follows from the above definition that θ and ( 90 - θ ) are complementary angles in trigonometry for an acute angle θ In ΔABC, ∠B = 90 0 ∴ ∠A + ∠C = 90 0 ∠C =90 0 - ∠A For the sake of easiness in this derivation, we will write ∠C and ∠A as C and A respectively Thus C = 90 0 - A sin A = BC / AC cosec A = AC / BC cos A = AB / AC sec A = AC / AB tan A = BC / AB cot A = AB / BC and sin C = sin (90 0 - A ) = AB / AC; cosec C = cosec (90 0 - A) = AC / AB cos C = cos (90 0 - A) = BC / AC; sec C = sec (90 0 - A) = AC / BC tan C = tan (90 0 - A) = AB / BC; cot C = cot (90 0 - A) = BC /AB
This means, for example sin 70 0 = cos 20 0 The cofunction of the sine is the cosine. And 20° is the complement of 70°. Some Solved Examples on complementary angles in trigonometry : 1) Evaluate : cos 37 0 / sin 53 0 Solution : cos 37 0 /sin 53 0 = cos( 90 – 53 )/sin 53 = sin 53 0 /sin 53 0 = 1 ________________________________________________________________ 2) Show that : ( cos 70 0 ) / (sin 20 0 ) + (cos 59 0 ) / sin 31 0 - 8 sin 2 30 0 = 0 Solution : Consider ( cos 70 0 ) / (sin 20 0 ) + (cos 59 0 ) / sin 31 0 - 8 sin 2 30 0 = [ cos ( 90 0 - 20 0 )] / [sin 20 0 ] + [ cos(90 0 - 31 0 )] / sin 31 0 - 8 x(1/2) 2 = sin 20 0 / sin 20 0 + sin 31 0 / sin 31 0 - 8 x 1/ 4 = 1 + 1 – 2 = 0 ∴ ( cos 70 0 ) / (sin 20 0 ) + (cos 59 0 ) / sin 31 0 - 8 sin 2 30 0 = 0 Trigonometry • SOHCAHTOA -Introduction to Trigonometry • Trigonometric ratios and their Relation • Trigonometry for specific angles • Complementary angles in Trigonometry • Trigonometric Equations Covid-19 has affected physical interactions between people. Don't let it affect your learning.
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