# Trigonometry Reviewer 1 Essay

Angles and Measures • Angle – is formed by two rays with a common endpoint. • Standard Position: An angle inscribed in a circle whose center is at the origin is said to be in “standard position” if one of the sides of the angle coincides with the positive ray of the x-axis. • Stationary Ray – “Initial Side” of the angle (the x-axis, abscissa side; the one that is NOT MOVING; the starting point of every angle) • Rotating Ray – “Terminal Side” of the angle (the one that MOVES, “rotates.”) • Angle Directions – o Counter – clockwise: POSITIVE (+) o Clockwise: NEGATIVE (−) o Quadrantal Angle: the terminal side (rotating ray) is in the coordinate system, which means

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Points on the Unit Circle • Abscissa – x-axis • Ordinate – y-axis • Use the Pythagorean Theorem in finding the coordinates of a point on the Unit Circle. o 12 = x2 + y2 • The arrangement of coordinates of point: ( x , y )

Sine and Cosine Functions • Cosine: The “x-axis” (abscissa) • Sine: The “y-axis” (ordinate) • The Special Right Triangles: o 30° – 60° – 90° and 60° – 30° – 90° Triangles: ▪ 30° (√3/2 , ½) ▪ 60° (½ , √3/2) ▪ 90° (0 , 1) o 45° – 45° – 90° Triangle: ▪ 45° (√2/2, √2/2) ▪ 90° (0 , 1) • If the degree-angle is not part of the Special Right Triangles: Use the CALCULATOR ( o RMINDER: Round-off to the nearest 4th decimal place. • If in radiant form: CONVERT FIRST TO DEGREE, THEN SOLVE.

Graph of Sine Function • y = a sin b θ o a: changes the amplitude, max. point, and the min. point of