GMAT GRE 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th grade math 8th grade math 9th grade math 10th grade math 11th grade math 12th grade math Precalculus Worksheets Chapter wise Test MCQ's Math Dictionary Graph Dictionary Multiplicative tables Math Teasers NTSE Chinese Numbers CBSE Sample Papers 
Complementary angles in TrigonometryCovid19 has led the world to go through a phenomenal transition . Elearning 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 Covid19 has affected physical interactions between people. Don't let it affect your learning.
More To Explore

