Day and date : Tuesday 10 / 5 / 2011

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Day and date : Tuesday 10 / 5 / 2011 Zayed Al -Thani School Revision of the unit (Trigonometry part 1 ) مراجعة الوحدة ( حساب المثلثات الجزء الأول ) Objectives : 1 ) To find the basic trigonometric ratios of a given angle in a right angled triangle using the definitions To use trigonometry and a scientific calculator to find the length of the unknown sides in a right angled triangle 3) To use trigonometry and a scientific calculator to find the size of the unknown angles in a right angled triangle 1) إيجاد النسب المثلثية الأساسية لزاوية محددة في مثلث قائم الزاوية باستخدام التعريف 2 ) استخدام حسلب المثلثات والآلة الحاسبة في إيجاد اطوال الأضلاع المجهولة في المثلث القائم 3 ) استخدام حسلب المثلثات والآلة الحاسبة في إيجاد قياس الزوايا المجهولة في المثلث القائم الأهداف :

Day and date : Tuesday 10 / 5 / 2011 Definitions : التعريفات : hypotenuse hypotenuse opposite opposite adjacent adjacent

α 10 6 θ 8 Example : Day and date : Tuesday 10 / 5 / 2011 Use the figure to find the following trigonometric ratios : استخدم الشكل وأوجد النسب المثلثية التالية : α 10 6 θ 8

θ α Work sheet ( 1 ) α 𝑥 = 𝑥 θ Day and date : Tuesday 10 / 5 / 2011 A ) Use the given figure to find the following trigonometric ratios : أ ) استخدم الشكل وأوجد النسب المثلثية التالية : 12 cm α 5 cm 13 cm θ B ) Use the Pythagorean theorem to find the missing side then find the following trigonometric ratios ب ) استخدم نظرية فيثاغورس وأوجد الضلع الناقص ثم أوجد النسب المثلثية التالية : α 𝑥 = 25 cm 𝑥 θ 24 cm

Day and date : Tuesday 10 / 5 / 2011 Trigonometry and scientific calculators Use a scientific calculator to find the following trigonometric ratios : ∘ استخدم آلة حاسبة علمية وأوجد : Sin 40 ≈ 0.6428 Press sin 40 = ∘ ' " Cos 37 18 15 ≈ 0.7954 Press cos 37 18 15 = ∘ , , , ∘ , , , ∘ , , , ∘ ' Tan 67 33 ≈ 2.4202 Press tan 67 33 = ∘ , , , ∘ , , ,

Day and date : Tuesday 10 / 5 / 2011 Trigonometry and scientific calculators The option of the inverse trigonometric ratios is used to find an unknown angle ميزة معكوس النسبة المثلثية تستخدم لإيجاد الزاوية المجهولة Find the angle θ ( to the nearest degree ) given that : أوجد الزاوية علما ً أن : θ ∘ Sin θ = 0.6432 θ = 40.03 ≈ 40 Press shift sin 0.6432 = Sin ( read : sine inverse ) -1 tan θ = ∘ θ = 57.99 ≈ 58 Press shift tan 8 a b/c 5 =

Finding an unknown side Day and date : Tuesday 10 / 5 / 2011 Finding an unknown side Find the length of the unknown sides ( to 1 d.p. ) in the figure below : أوجد الأطوال المجهولة في الشكل التالي ( لأقرب منزلة عشرية ) : y 𝑥 37 12 cm

Work sheet ( 2 ) y 𝑥 α θ Day and date : Tuesday 10 / 5 / 2011 A ) Find the unknown sides in the figure below ( to 1 d.p. ) : أ ) أوجد الأضلاع المجهولة في الشكل المجاور ( لأقرب منزلة عشرية ) : y ∘ 30 8 cm 𝑥 B ) Find ( to the nearest degree ) the size of the unknown angles in the triangle below : ب ) أوجد ( لأقرب درجة ) قياس الزوايا المجهولة في المثلث ادناه : α 25 cm θ 24 cm By : Mohammad Badawi Math department hamadaa_math@yahoo.com

Finding an unknown angle Day and date : Tuesday 10 / 5 / 2011 Finding an unknown angle Find the size of the unknown angles ( the nearest degree ) in the figure below : أوجد قياس الزوايا المجهولة في الشكل التالي ( لأقرب درجة ) : α 16 cm 𝑥 θ 10 cm

Work sheet ( 2 ) y 𝑥 α θ Day and date : Tuesday 10 / 5 / 2011 A ) Find the unknown sides in the figure below ( to 1 d.p. ) : أ ) أوجد الأضلاع المجهولة في الشكل المجاور ( لأقرب منزلة عشرية ) : y ∘ 30 8 cm 𝑥 B ) Find ( to the nearest degree ) the size of the unknown angles in the triangle below : ب ) أوجد ( لأقرب درجة ) قياس الزوايا المجهولة في المثلث ادناه : α 25 cm θ 24 cm By : Mohammad Badawi Math department hamadaa_math@yahoo.com