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Questions Over Section 1.5 Section 2.1 Right Triangle Trigonometry There are no conflicts between the right triangle definitions and the coordinate definitions. We will use both techniques throughout the term. Recall that complementary angles add to _________ Angle: Complementary Angle: A + B + C = ______ A A + B = ______ C A = B B = Cofunctions of complementary angles are equal. Examples: sin 30o = cos _______ tan 10o = cot _______ cos 7o = sin _______ csc 72o = sec _______ Simplify without a calculator: sin2 20o + sin2 70o Let's find the exact values of the six trigonometric functions for 30o and 60o . sin 30o = csc 30o = cos 30o = sec 30o = tan 30o = cot 30o = sin 60o = csc 60o = cos 60o = sec 60o = tan 60o = cot 60o = Section 2.2 Degrees and Minutes Example: Convert 24o 12' to decimal degrees. Example: Convert 18.6o to degrees and minutes. Working with degrees and minutes: Be able to add and subrtact Example: Find 24o 12' + 17o 56' Example: Find 180o - 16o 4' Calculating trig values with degrees and minutes: Example: Find tan(15o 11') Example: Find csc 30' Using Inverse Trigonometric Functions Inverse trig functions allow us to solve for the original angle. RECALL FROM ALGEBRA: solve: 3x = 12 solve x2 = 25 solve sinθ = 0.4 We will work hard with the inverse trig functions. Example: Solve cosθ = 0.9 Example: Solve cosθ = -0.2 Inverse cosine can give us a Quadrant I or a Quadrant II angle only. Later we will figure out how to get angles in other quadrants that are also solutions. Example: Find the acute angle θ so that secθ = 2.5. Section 2.3 Solving Right Triangles You may ignore the material on significant digits. NOTE: Because we will not be paying attention to significant digits, sometimes our answer will round differently than the back of the book. THAT IS OKAY! Example: Solve the right triangle given that A = 42o and c = 89 cm. Example: Solve the right triangle given that c = 45.54 feet and a = 23.32 feet. Example: Use the figure to find the measure of angle A. 45o A B Example: Use the following figure to find the value of x. Assume C is the center of the circle. C 26o 19 D x A