Geometry/TRIG Name: _________________________ Introduction to Trigonometry – Day 1 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: ______ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ q Identify each side: Hypotenuse: ______ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ 3. 4. n k q q q p a m j a Identify each side: Hypotenuse: ______ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____ Identify each side: Hypotenuse: ______ Opposite side of q: ____ Opposite side of a: ____ Adjacent side of q: ____ Adjacent side of a: ____

q Six Trigonometric Definitions: Sine: _____________________________________ __________________________________________ Notation: __________________________________ “Say It” : __________________________________ Cosine: ____________________________________ Tangent: ___________________________________ *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: _____ _____ _____ _____ _____ _____ _____ _____ _____ Page 2 q Set Up the 3 Trigonometric Ratios for q and a. _____________ ____________ q d c a b

_____________ ____________ x = _______ 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 20 12 q x = _______ _____________ ____________ x = _______ _____________ ____________

Homework: Into to Trig Day 1 Worksheet 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. 3. 9 4. 10 3 q q x 6 20 a x a x = _______ _____________ ____________ q = ________ a = _________ x = _______ _____________ ____________ Homework: Into to Trig Day 1 Worksheet

Introduction to Trigonometry – Day 2 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 ____________. Page 5 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) = ________ 2. cos(30) = ________ 3. tan(30) = ________ 4. sin(52) = ________ 5. cos(83) = ________ 6. sin(1) = ________ 7. tan(45) = ________ 8. sin(89) = ________ 9. cos(89) = ________ 10. tan(89) = ________ 11. sin-1(0.5) = ________ 12. cos-1 (0.5) = ________ 13. tan-1 (0.5) = ________ 14. sin-1 (2) = ________ 15. cos-1 (0.9) = ________ 16. tan-1 ( 3 4 ) = ________

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. x y x = _________ y = _________ Page 6

Homework: 1. Pg. 304 Self Test #3-7 2. Pg. 308 WE +1-6 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 35º 15 x 40º 12 x = ______ x = ______ 3) 4) x 20º 6.3 x 38º 14 x = ______ x = ______ 5) 6) x 25º 21 x 52º 35 q q y y x = ______ y = ______ q = ______ x = ______ y = ______ q = ______ Homework: 1. Pg. 304 Self Test #3-7 2. Pg. 308 WE +1-6 Page 7

Introduction to Trigonometry – Day 3 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 8

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 6 19 15 9 b b x q q x = _____ = _____  = _____ x = _____ = _____  = _____ 3) 4) y a a y 4 5 5 10 q q 12 y = _____ = _____ a = _____ y = _____ = _____ a = _____ Page 9