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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 2 4.3 Right Triangle Trigonometry Precalculus adj Precalculus opp 4.3 Right Triangle Trigonometry Trigonometric Functions hyp 3 4 4.3 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 = 5 YOU TRY • cos = • tan = • csc = • sec = Precalculus • sin = 4.3 Right Triangle Trigonometry • Evaluate the six trig functions of the angle shown in the right triangle • cot = 6 4.3 Right Triangle Trigonometry Precalculus Example 2 Find cos 𝜃 if tan 𝜃 = . 1 4 7 Precalculus Find sec 𝜃 if sin 𝜃 = 4.3 Right Triangle Trigonometry You Try 3 . 2 8 • sin 𝜋 6 • cos 120° • tan 45° csc 63° 2𝜋 sec 3 4.3 Right Triangle Trigonometry • Evaluating the following to the nearest hundredths using a calculator: Precalculus Example 3 cot 250° 9 Example 4 30° 15 4.3 Right Triangle Trigonometry Precalculus • Find the value of x for the right triangle shown x 10 c A b B 62° 6 C 4.3 Right Triangle Trigonometry • Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus Example 5 11 B c A 30° a 15 C 4.3 Right Triangle Trigonometry Precalculus You Try • Solve ∆ABC. 12 B 15 A 9 C 4.3 Right Triangle Trigonometry • Find the measure of angle B to the nearest tenth (ONE decimal place ). • . Precalculus Example 6 13 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 14 B c A 5 9 C 4.3 Right Triangle Trigonometry • Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus Example 7 15 B 12 A 2 C 4.3 Right Triangle Trigonometry Precalculus You Try • Solve ∆ABC. 16 17 4.3 Right Triangle Trigonometry Precalculus 18 4.3 Right Triangle Trigonometry Precalculus 19 4.3 Right Triangle Trigonometry Precalculus 20 4.3 Right Triangle Trigonometry Precalculus 21 4.3 Right Triangle Trigonometry Precalculus 22 4.3 Right Triangle Trigonometry Precalculus 23 4.3 Right Triangle Trigonometry Precalculus 24 4.3 Right Triangle Trigonometry Precalculus 25 4.3 Right Triangle Trigonometry Precalculus 26 4.3 Right Triangle Trigonometry Precalculus 4.3 Right Triangle Trigonometry Precalculus Victory Lap Find the unknown value: 27