4 3 Right Triangle Trigonometry Objectives Evaluate trigonometric

4. 3 Right Triangle Trigonometry Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric functions to model and solve Precalculus 4. 3 Right Triangle Trigonometry real-life problems

Trigonometric Functions Given a right triangle with acute angle opp hyp adj Precalculus 4. 3 Right Triangle Trigonometry 2

Example 1 · Evaluate the six trig functions of the angle shown in the right triangle 5 13 · sin = · cos = · tan = · csc = · sec = 12 · cot = Precalculus 4. 3 Right Triangle Trigonometry 3

Example 2 · Find the value of x for the right triangle shown 30° 15 x Precalculus 4. 3 Right Triangle Trigonometry 4

Example 3 · Solve ∆ABC c A Precalculus b B 62° 6 C 4. 3 Right Triangle Trigonometry 5

You Try · Solve ∆ABC B c A Precalculus 30° a C 4. 3 Right Triangle Trigonometry 6

Special Triangles 30º-60°-90° 60° 1 Recall the conversions 2 30°= 60°= 30° Precalculus 4. 3 Right Triangle Trigonometry 7

Special Triangles 45º-45°-90° Recall the conversion 45°= 1 45° 1 Precalculus 4. 3 Right Triangle Trigonometry 8

Co-functions of Complementary Angles · Look back at the sines and cosines for the 30 -60 -90 triangle · Note that sin 30°=cos 60° · Co-functions of complementary angles are equivalent Precalculus 4. 3 Right Triangle Trigonometry 9

Trigonometric Identities · Reciprocal Identities Precalculus 4. 3 Right Triangle Trigonometry 10

Trigonometric Identities · Quotient Identities Precalculus 4. 3 Right Triangle Trigonometry 11

Trigonometric Identities · Pythagorean Identities Note: sin 2 is (sin )2 not sin ( 2) Precalculus 4. 3 Right Triangle Trigonometry 12

Example 4 · Given sin =0. 6, find the value of cos · Given sin =0. 6, find the value of tan Precalculus 4. 3 Right Triangle Trigonometry 13

Example 5 Use trigonometric identities to transform one side of the equation into the other. · cos sec =1 · (sec +tan )(sec -tan )=1 Precalculus 4. 3 Right Triangle Trigonometry 14

Surveying · A surveyor is standing 50 ft from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71. 5°. How tall is the tree? Precalculus 4. 3 Right Triangle Trigonometry 15

River Walk · You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle ө between this path and the river’s edge. Precalculus 4. 3 Right Triangle Trigonometry 16

Skateboarding · Find the length c of the skateboard ramp. Precalculus 4. 3 Right Triangle Trigonometry 17

Homework · Star Wars Worksheet · Page 285 44 -54 even, 79 -82 all Precalculus 4. 3 Right Triangle Trigonometry 18