1. 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: ____

2. 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

3. _____________ ____________ 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 = _______
_____________ ____________

4. 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

5. 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 ) = ________

6. 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

7. 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

8. 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

9. 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