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41 Right Triangle Trigonometry Precalculus Knight’s Charge: 1 Sec 4.1: Right Triangle Trigonometry Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric functions to model and solve real-life problems 3 41 Right Triangle Trigonometry Precalculus adj Precalculus opp 41 Right Triangle Trigonometry Trigonometric Functions hyp 4 5 41 Right Triangle Trigonometry Precalculus Example 1 • cos = • tan = • csc = 5 13 12 • sec = Precalculus • sin = 4.3 Right Triangle Trigonometry • Evaluate the six trig functions of the angle shown in the right triangle • cot = 6 YOU TRY • cos = • tan = • csc = • sec = Precalculus • sin = 41 Right Triangle Trigonometry • Evaluate the six trig functions of the angle shown in the right triangle • cot = 7 41 Right Triangle Trigonometry Precalculus Example 2 Find cos 𝜃 if tan 𝜃 = . 1 4 8 Precalculus Find sec 𝜃 if sin 𝜃 = 41 Right Triangle Trigonometry You Try 3 . 2 9 6 • cos 120° 2𝜋 sec 3 • tan 45° cot 250° 41 Right Triangle Trigonometry • Evaluating the following to the nearest hundredths using a calculator: 𝜋 csc 63° • sin Precalculus Example 3 10 Example 4 30° 15 41 Right Triangle Trigonometry Precalculus • Find the value of x for the right triangle shown x 11 c A b B 62° 6 C 41 Right Triangle Trigonometry • Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus Example 5 12 B c A 30° a 15 C 41 Right Triangle Trigonometry Precalculus You Try • Solve ∆ABC. 13 B 15 A 9 C 41 Right Triangle Trigonometry • Find the measure of angle B to the nearest tenth (ONE decimal place ). • . Precalculus Example 6 14 B 12 A 15 C 4.3 Right Triangle Trigonometry Find the measure of angle A to the nearest hundredths (TWO decimal places ). Precalculus You Try 15 B c A 5 9 C 41 Right Triangle Trigonometry • Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus Example 7 16 B 12 A 2 C 41 Right Triangle Trigonometry Precalculus You Try • Solve ∆ABC. 17 18 41 Right Triangle Trigonometry Precalculus 19 4.3 Right Triangle Trigonometry Precalculus 20 41 Right Triangle Trigonometry Precalculus 21 41 Right Triangle Trigonometry Precalculus 22 41 Right Triangle Trigonometry Precalculus 23 41 Right Triangle Trigonometry Precalculus 24 41 Right Triangle Trigonometry Precalculus 25 41 Right Triangle Trigonometry Precalculus 26 41 Right Triangle Trigonometry Precalculus 27 4.3 Right Triangle Trigonometry Precalculus 4.3 Right Triangle Trigonometry • Go to any “letter”… only two people per letter. • You must write down your letter, equation, and answer for each problem. • Do not move stations until I tell you to! Precalculus Round Robin 28 4.3 Right Triangle Trigonometry Precalculus Victory Lap Find the unknown value: 29