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MAT 182 Chapter 1 Fitzgerald Sect 1.1 Angle: Standard Position: Quadrantal Angles: Acute Angle: Right Angle: Obtuse Angle: Straight Angle: Complementary Angles: Supplementary Angles: Find the complement and supplement angles of 40o. 1 MAT 182 Chapter 1 Fitzgerald 2 Solve for x and y. 6x 1 2x 1 7 y 11 9y 25 Breaking down a degree. Minute: Second: Perform each calculation. 5129'3246' 90 1837' Converting Degrees, Minutes, and Seconds to a decimal degree and vise versa. Convert 21 8' 14" Convert 34.2678 to degrees, to a decimal degree. Minutes, and seconds to nearest sec. MAT 182 Chapter 1 Fitzgerald 3 Coterminal Angles: Assume the following angles are in standard position. Find a positive angle less than 360o that is coterminal with each of the following: a. a 400o angle. b. a – 855o angle. CD players always spin at the same speed. Suppose a player makes 480 revolutions per min. Through how many degrees will a point on the edge of the CD move in 2 seconds? Sect. 1.2 Angle Relationships 1 2 3 4 5 Vertical Angles: Corresponding Angles: Alternate Interior Angles: Alternate Exterior Angles: Same Side Interior Angles: 7 6 8 MAT 182 Chapter 1 Fitzgerald 4 Sum of the angles of a triangle_____________________________________. Types of Triangles: Angles Acute Triangle: Right Triangle: Obtuse Triangle: Sides Equilateral Triangle: Isosceles Triangle: Scalene Triangle: Similar Triangles: Conditions: Labeling: ABC ~ RST MAT 182 Chapter 1 Fitzgerald 5 Sect. 1.3 Trigonometric Functions. Definitions of Trigonometric Functions of Any Angle Let be any angle in standard position and let P = (x, y) be a point on the terminal 2 2 side of . If r x y is the distance from (0, 0) to (x, y), the six trigonometric functions of are defined by the following ratios: Let P = (8, 15) be a point on the terminal side of . Find each of the six trigonometric functions of . P = (8, 15) is a point on the terminal side of . x = 8 and y = 15. MAT 182 Chapter 1 Fitzgerald Let P = (1, –3) be a point on the terminal side of . Find each of the six trigonometric functions of . P = (1, –3) is a point on the terminal side of . x = 1 and y = –3. 6 MAT 182 Chapter 1 Fitzgerald 7 Section 1.4 Reciprocal Identities. sin csc cos sec tan cot Find the sign value of the trigonometric functions for each quadrant and the range values of the six trigonometric functions. y sin y csc y cos y sec y tan y cot Suppose sin functions. y sin y cos y x y tan y cot y sec y csc 2 and tan 0 . Find the values of the other five trigonometric 3 MAT 182 Chapter 1 Pythagorean Identities. x2 y 2 r 2 Quotient Identities. sin cos Fitzgerald 8 r x2 y 2 x2 y 2 r 2 x2 y 2 r 2 x2 y 2 r 2 cos sin Find sin and tan , given that cos 3 4 and sin 0 . Find sin and cos , given that tan 43 and is quadrant 3.