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Notes 6.2 – Right Triangle Trig. Algebra III Honors Date: _________ Goal: Trigonometric functions can be thought of as another way to measure angles. The functions are the ratio of the sides formed by a given angle. So, if the angle is set, then the sides will always form certain ratios. sin csc cos sec tan cot Example 1: Find all six trigonometric function values for a 45 angle. Example 2: Find all the trigonometric functions values for a 30 and 60 angle. Example 3: Use a calculator to evaluate the following trig function values: a) sin 76.4 b) sec 32.7 c) tan 145 d) cot 398 e) cos 3.5 f) csc 0.5 g) sin 2.1 h) cot 2π Reciprocal Identities 1 1 tan x , cot x , cot x tan x sin x 1 , csc x csc x 1 , sin x cos x 1 , sec x sec x 1 cos x Pythagorean Identities sin 2 cos 2 1 1 tan 2 sec 2 1 cot 2 csc 2 Quotient Identities sin tan cos cos cot sin Example 4: Let θ be an acute angle such that sin θ = 0.6; find the values of a) cos θ and b) tan θ. Example 5: Let θ be an acute angle such that tan θ = 1/3 find the values of a) cot θ, and b) sec θ. Example 6: Use the trigonometric identities to transform the left side of the equation in to the right side of the equation. a) sin θcsc θ = 1 b) (csc θ + cot θ)(csc θ – cot θ) = 1 Applications Example 7: A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3 . How tall is the Washington Monument? Example 8: A historic lighthouse is 200 yards from a bike path along the edge of a lake. A walkway to the lighthouse is 400 yards long. Find the acute angle θ between the bike path and the walkway. Homework: p. 443 – 445 # 4 – 64 M4 # 67, 70 Notes 6.2 – Right Triangle Trig. Algebra III Honors Name: __________ Date: _________ Skills Check. All problems are no calculator unless otherwise specified. Find the exact value for the following trig functions. 1) sec 45 2) sin 30 3) cos 60 Find the approximate values for the following: (Calculator) 4) cos 24.5 5) csc 125.7 6) cot 2.3 7) Let θ be an acute angle such that cos θ = 0.25, find the values of a) sin θ and b) tan θ. 8) Use trig identities to transform the left side into the right side of the equation: tan θ csc θ = sec θ 9) You are standing 45 meters from the base of the Empire State building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 . The total height of the building is another 123 meters above the 86th floor. What is the approximate height of the building? (Calculator)