Introduction to Trigonometry

1. Introduction to Trigonometry Lesson 9.9

2. What is Trigonometry? • The shape of a right triangle is determined by the value of either of the other two angles. • This means that once one of the other angles is known, the ratios of the various sides are ALWAYS the same regardless of the size of the triangle. • These ratios are described by following “trigonometric functions” of the known angle. • This means that if one angle and one side length is known, all other angles and side lengths can be determined. • OR… it means that if two sides of the triangle are known, the third side and all other angles can be determined.

3. Three Trigonometric Ratios B • Sine of A = sin A = opposite leg = hypotenuse • Cosine of A = cosA = adjacent leg = hypotenuse • Tangent of A = tan A = opposite leg = adjacent leg a c A b C a c b c a b

4. Memorizethis… Sine Opposite Hypotenuse S O H C A H T O A Cosine Adjacent Hypotenuse Tangent Opposite Adjacent

5. Memorizethis… S O H C A H T O A PPOSITE DJACENT OSINE PPOSITE ANGENT YPOTENUSE I N E YPOTENUSE DJACENT

6. Find cosA • By the Pythagorean Theorem find side c. • c = 13 • cosA = adjacent leg to A = hypotenuse 12 13 Find tan B • tanB= leg opposite B = leg adjacent to B 12 5

7. ΔABC is an isosceles triangle as marked. Find sin C. • Draw in an altitude to make a right triangle. • Use the Pythagorean Theorem to find the length of the altitude. • AD = 20 • Sin C = opposite = hypotenuse A 25 25 20 B C 15 15 30 20 = 425 5

8. Use the fact that tan 40º ≈ 0.8391 to find the height of the tree to the nearest foot. • Tan 40º = opposite = adjacent • 0.8391 ≈ h 50 • 0.8391(50) ≈ h • 41.955 ≈ h • The tree is ≈ 42 feet tall. h50

9. Video Time…