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UNIT 11: INTRO TO TRIG PART 1 Let's start with a quick review of the three trigonometric functions we already understand. Remember that these functions work only in right triangles. where A represents the angle of reference. These formulas ONLY work in a right triangle. The hypotenuse is always across from the right angle. Check the question for how to round your answer. You will need a scientific or graphing calculator. Trigonometric Ratios in the Calculator: Find sin 35° Find <A to the nearest degree, Set MODE to Degree given cos A = 3/5 Type entry on the Home Screen Set MODE to Degree Type entry on the Home Screen. Hit 2nd cos to get the cos-1 Degrees, Minutes, and Seconds (DMS): Angles are measured in degrees, minutes, and seconds. Degrees Degrees-Minutes-Seconds Where do you find all the degree, minute, and second buttons in the calculator? Standard Position: An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side. If the terminal side of an angle lies "on" the axes (such as 0º, 90º, 180º, 270º, 360º ), it is called a quadrantal angle. The angle shown below is referred to as a Quadrant II angle since its terminal side lies in Quadrant II. The angle is measured by the amount of rotation from the initial side to the terminal side. If measured in a counterclockwise direction the measurement is positive. If measured in a clockwise direction the measurement is negative. If two angles in standard position have the same terminal side, they are called coterminal angles. (add or subtract 360o) Angle of Elevation: line of sight is titled upward angle of elevation forms a right angle horizontal line Angle of Depression: line of sight is titled downward horizontal line angle of depression forms a right angle horizontal line **angle of elevation = angle of depression** TRIGONOMETRY RADICALS IN THE FIRST QUADRANT 30 sin cos tan 45 1 2 3 2 3 3 60 2 2 2 2 3 2 1 2 1 3 REFERENCE ANGLE – the positive acute angle formed from the terminal side of an angle and the x-axis. (quickest angle back to the x-axis!) ASTC – shows you where the trig functions (sine, cosine, tangent) are positive or negative. UNIT CIRCLE – a circle with a radius of 1 ( x, y ) cos , sin cos x sin y y sin tan x cos