Outside the middle school program / Trigonometry 4 exercises (including 3 corrected)

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ABC¸o 1. Properties E.5671 Consider the triangle ABC right-angled C shown below : 1 Express the trigonometric ratios : cos ¸ o ; sin ¸ o ; tan ¸ o 2 a Establish the following equality: cos ¸ 2 + sin ¸ 2 = 1 b Establish the following equality: tan ¸ = sin ¸ cos ¸ 2. Notable Angles and Square Roots E.709 1 Construct a triangle ABC equilateral with side 4 cm . Let H be the foot of the height from A . 2 Give the exact value of the length AH . 3 Determine the exact value of sin (60 o ) in the triangle ACH E.715 The unit of length is the centimeter 1 Construct a triangle DOS such that : DS = DO = 6 ; ODS = 120 o What is the nature of the triangle DOS ? Justify. 2 In triangle DOS , draw the height coming from D . It intersects [ OS ] at H . The following table is given : x 0 o 30 o 45 o 60 o 90 o cos x 1 √ 3 2 √ 2 2 1 2 0 sin x 0 1 2 √ 2 2 √ 3 2 1 tan x 0 √ 3 3 1 √ 3 × a Calculate the exact value of OH . b Deduce that : OS =6 3 3 Place the point M of [ DS ] such that SM =5 . Draw the parallel to ( OS ) passing through M ; it intersects [ DO ] at N . Calculate the exact value of MN . E.707 Let C be a circle of center O and radius 4 cm . Let B and C be two diametrically opposed points and A a third point of the circle such that AC =4 cm . 1 Draw the picture. 2 Show that the triangle ABC is right-angled. The triangle ABC has an area equal to 8 2 . 3 Deduce the length of [ AB ] . 4 Calculate the measure of ABC . Let A be the symmetric of A relative to the ( BC ) axis. Note H the point of intersection of [ AA ] and ( BC ) . 5 Show that : ABA =60 o 6 Show that ABA is an equilateral triangle. https://chingmath.fr sacados/5671 ABC¸o chapExoCorrec/709 sacados/709 chapExoCorrec/715 sacados/715 ?? - 2004 - 7 points chapExoCorrec/707 sacados/707