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

Precalculus 4.3 Right Triangle Trigonometry

Trigonometric Functions hyp Precalculus opp  adj 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Example 1 Precalculus Evaluate the six trig functions of the angle  shown in the right triangle sin  = cos  = tan  = csc  = sec  = cot  = 4.3 Right Triangle Trigonometry 5 12 13 

YOU TRY Precalculus Evaluate the six trig functions of the angle  shown in the right triangle sin  = cos  = tan  = csc  = sec  = cot  = 4.3 Right Triangle Trigonometry

Example 2 Find cos 𝜃 if tan 𝜃 = 1 4 . Precalculus 4.3 Right Triangle Trigonometry

You Try Find sec 𝜃 if sin 𝜃 = 3 2 . Precalculus 4.3 Right Triangle Trigonometry

Example 3 Evaluating the following to the nearest hundredths using a calculator: sin 𝜋 6 cos 120° tan 45° Precalculus csc 63° sec 2𝜋 3 cot 250° 4.3 Right Triangle Trigonometry

Example 4 30° 15 x Find the value of x for the right triangle shown Precalculus x 15 30° 4.3 Right Triangle Trigonometry

Example 5 Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus A B C 62° 6 c b 4.3 Right Triangle Trigonometry

You Try B c a 30° A C Solve ∆ABC. Precalculus 4.3 Right Triangle Trigonometry

Example 6 Find the measure of angle B to the nearest tenth (ONE decimal place ). . Precalculus A B C 9 15 4.3 Right Triangle Trigonometry

You Try Find the measure of angle A to the nearest hundredths (TWO decimal places ). Precalculus A B C 12 4.3 Right Triangle Trigonometry 15

Example 7 Solve ∆ABC (i.e. find the measures of all the unknown angles and sides of the triangle). Precalculus A B C 9 c 5 4.3 Right Triangle Trigonometry

You Try B 12 A C Solve ∆ABC. Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Precalculus 4.3 Right Triangle Trigonometry

Victory Lap Find the unknown value: Precalculus 4.3 Right Triangle Trigonometry