Introduction to Trigonometry

Geometry/TRIG Introduction to Trigonometry Name: _________________________ Date: __________________________ Trigonometry: __________________________________________________________ ______________________________________________________________________ Vocabulary for Sides of a Right Triangle: Hypotenuse: ___________________________________________________________ Opposite: _____________________________________________________________ Adjacent: _____________________________________________________________ Examples: b, c, d… p, q refer to side lengths. q and a refer to angle measures. 1. 2. h a q d c a f g b Identify each side: Hypotenuse: ______ q Identify each side: Opposite side of q: ____ Hypotenuse: ______ Opposite side of a: ____ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ 3. Adjacent side of q: ____ Adjacent side of a: ____ n 4. k q q p m a q j a Identify each side: Identify each side: Hypotenuse: ______ Hypotenuse: ______ Opposite side of q: ____ Opposite side of a: ____ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ Six Trigonometric Definitions: Page 2 Sine: _____________________________________ __________________________________________ q Notation: __________________________________ “Say It” : __________________________________ Cosine: ____________________________________ __________________________________________ Notation: __________________________________ “Say It” : __________________________________ Tangent: ___________________________________ __________________________________________ Notation: __________________________________ “Say It” : __________________________________ *Cosecant: the reciprocal of the _______________ function. ________________________ *Secant: the reciprocal of the _________________ function. ________________________ *Cotangent: the reciprocal of the ______________ function. ________________________ *We will not focus on these three in this course. You will see them again in future courses. Commonly Used Acronym to Remember the first 3 Trigonometric Definitions: _____ _____ _____ _____ _____ _____ _____ _____ _____ Set Up the 3 Trigonometric Ratios for q and a. q c d a _____________ ____________ _____________ ____________ _____________ ____________ b Examples: For each diagram, first find the missing side length. Next set up the trig ratios (sine, cosine, and tangent) for the angles labeled q and a. REDUCE all ratios. Page 3 x 1. 2. a q x 5 16 a 12 20 q x = _______ x = _______ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ 3. 4. 9 10 3 q q 6 20 x a x a x = _______ x = _______ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ _____________ ____________ q = ________ a = _________ Page 4 Calculator Practice: The calculator has the trig functions, sine, cosine, and tangent, built into them. The calculator recognizes two different units of measure for angles used in trig functions: ___________ and ____________. In this class we will always use ____________. Practice using your calculator to find the following values. Round all values to the nearest hundredth. If you get an error message, make a note of it. 1. sin(30) = ________ 5. cos(83) = ________ 9. cos(89) = ________ 13. tan-1 (0.5) = ________ 2. 3. cos(30) = ________ 6. tan(30) = ________ 7. sin(1) = ________ 10. tan(89) = ________ 14. sin-1 (2) = ________ tan(45) = ________ 4. sin(52) = ________ 8. sin(89) = ________ 11. 12. sin-1(0.5) = ________ cos-1 (0.5) = ________ 15. 16. cos-1 (0.9) = ________ 3 4 tan-1 ( ) = ________ EXAMPLES: Using trigonometric equations to solve for side lengths in right triangles. Example 1 – Find side lengths. x x = _________ y = _________ y Example 2 – Find side lengths. x x = _________ y = _________ y Example 3 – Find side lengths. y x x = _________ y = _________ Page 5 PRACTICE: Using trigonometric equations to solve for side lengths in right triangles. Directions: Set up trigonometric ratios and other equations to find each missing measurement. Round all decimal answers to the nearest hundredth. Show all work. 1) 2) x 15 x 35º 40º 12 x = ______ 3) x = ______ 4) x 6.3 38º x 20º 14 x = ______ 5) x = ______ 6) x q x y 25º q y 52º 21 35 x = ______ x = ______ y = ______ y = ______ q = ______ q = ______ Page 6 EXAMPLES: Using trigonometric equations to solve for angle measures in right triangles. Example 1 – Find angle measures. a x q x = _________ q = _________ a = _________ Example 2 – Find angle measures. a x q x = _________ q = _________ a = _________ Example 3 – Find angle measures. a x q x = _________ q = _________ a = _________ Page 7 PRACTICE: Using trigonometric equations to solve for angle measures in right triangles. Directions: Set up trigonometric and other equations to solve for each missing measurement. When possible, side lengths should be written as simplified square roots. Round all angle measures to the nearest hundredth. Show all work. 1) 2) x   19 9 q q 6 x = _____ x = _____ q = _____ q = _____  = _____  = _____ 3) 5 x 15 4) a y a y 4 5 10 q q 12 y = _____ y = _____ q = _____ q = _____ a = _____ a = _____ 5)  41 x x = _____ a = _____ a 40  = _____ Page 8