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#1 Notes 13.1 Right Triangle Trigonometry #1 Algebra 2 Notes 13.1 Right Triangle Trigonometry Algebra: the study of mathematics in which letters and other symbols are used to represent number and quantities in formulas and equations Geometry: the study of mathematics that deals with points, lines, angles, surfaces, and solids Trigonometry: the study of mathematics that deals with the relations between the sides and angles of triangles [right and nonright triangles] Consider a Right Triangle, one of whose acute angles [less than 90 o ] is 0 . 0 is a Greek letter and pronouned "Theta" other Greek letters: Alpha Beta Gamma Theta The three sides of a triangle are the Hypotenuse, the side opposite 0 , and the side next to 0 called the adjacent side [Abbreviated as HYP, OPP, ADJ] Name the sides of each triangle: 1) 2) OPP ADJ HYP 3) Ratios [Fractions] of a right triangle's 3 sides are used to define the six Trigonometric Functions: Trigonometric Functions and their abbreviations: Sine Cosecant Cosine Secant Tangent Cotangent Let 0 be an acute angle of a right triangle. The 6 [Trig] Trigonometric functions of 0 are defined as follows: Sin = Csc = Cos = Sec = Tan Cot = = Note:These last 3 functions are reciprocals of the first 3 This is where SOHCAHTOA comes from Remember: Pythagorean Theorem a 2 + b2 = c 2 Note: adj = adjacent opp = opposite hyp = hypotenuse Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 1. 3 4 2. 3 6 1 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 3. 52 5 4. 7 15 1 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember 5. 19 9 6. 15 9 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember 7. 24 16 8. 6 3 5 #1 Notes 13.1 Right Triangle Trigonometry #1 Algebra 2 Notes 13.1 Right Triangle Trigonometry Algebra: the study of mathematics in which letters and other symbols are used to represent number and quantities in formulas and equations Geometry: the study of mathematics that deals with points, lines, angles, surfaces, and solids Trigonometry: the study of mathematics that deals with the relations between the sides and angles of triangles [right and nonright triangles] Consider a Right Triangle, one of whose acute angles [less than 90 o ] is 0 . 0 is a Greek letter and pronouned "Theta" other Greek letters: Alpha Beta Gamma Theta The three sides of a triangle are the Hypotenuse, the side opposite 0 , and the side next to 0 called the adjacent side [Abbreviated as HYP, OPP, ADJ] Name the sides of each triangle: 1) 2) 3) Ratios [Fractions] of a right triangle's 3 sides are used to define the six Trigonometric Functions: Trigonometric Functions and their abbreviations: Sine Cosecant Cosine Secant Tangent Cotangent Let 0 be an acute angle of a right triangle. The 6 Trigonometric [Trig] functions of 0 are defined as follows: Sin = Csc = Cos = Sec = Tan Cot = = Note:These last 3 functions are reciprocals of the first 3 This is where SOHCAHTOA comes from Remember: Pythagorean Theorem a 2 + b2 = c 2 Note: adj = adjacent opp = opposite hyp = hypotenuse Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 1. 3 4 2. 3 6 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 3. sin = 52 5 5 1 2 = cos = tan = 5 = 1 5 csc = 2 sec = 2 cot = 4. 1 7 15 15 7 15 7 15 15 = 15 = 4 11 44 15 7 7 = 47 11 = 7 44 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 5. 19 9 6. 15 9 1 Evaluate the 6 Trig functions of the angle 0 shown in the right triangle: Remember to rationalize your answers 7. 24 16 162 + adj2 = 242 256 + adj2 = 576 256 256 adj2 = 320 adj = 320 adj = 8 5 8. 6 3 5 1