Pre-Calc Ch. 10-12 Unit Circle/Trig EQUATIONS
Unit circle: quadrants? If an angle is negative, it moves? Positive angles moves? Order of angles in each quadrant? (4) (x, y) value of pie/6? Pie/4? Pie/3? Pie/2? X, y values for pie? 2pie? Odd pie numbers always have the value? Ex. Pie, 3pie, 5pie. Even number pie always have the value? Ex. 2pie, 4pie.
1/2/3/4, left to right, right to left, 6/4/3/2, (√3/2, 1/2) (√2/2, √2/2) (1/2, √3/2) (0,1) (-1,0) (1,0), (-1,0) (1,0)
Reference angles: to find angle in quadrant 2, subtract the angle from? (2) To find an angle in quadrant 3, subtract by? (2) to find quadrant 4, subtract by? (2) Ex. Reference angle of 213 is?
180/pie, 180/pie, 360/2pie, 33,
Degrees to radians equation? Radians to degrees? pie in degrees? 2pie? pie/2? pie/6? Pie/4? Pie/3? How to do you find coterminal angles? (2) main ratio for degree to radian and radian to degree conversion?
Angle x pie radians/180 degrees, radians x 180 degrees/ pie radians180, 360, 90, 30, 45, 60, ads/subtract 2pie, pie/180
Even functions are? (2) odd functions are, (4) odd function: when you plug in -theta, this makes the function? Inverse functions: ex. Tan (-5) = 1.19 +npie. Or: given range (-infinity, infinity) and sin (x) = -1/2, the answer is? (2)
Cos/sec, sin/csc/tan/cot, negative, 7pie/6 + 2npie/ 11pie/6 + 2npie,
For finding the sin, trig value of angles like (13pie/6), what do you do? Special Angles: cos and sin of 30? cos and sin of 60? cos and sin of 45? Tan 30? Tan 60? Tan 45? 30 in pie rad? 60? 45?
Find coterminal angles and solve, (√3/2, 1/2) (1/2, √3/2), (√2/2, √2/2), √3/3, √3, 1, pie/6, pie/3, pie/4,
For evaluating trig functions of an angle: use trig? Ex. Given tan = -1, plug into the equation? The triangles at each quadrant form a?
Identities, 1 + tan^2 = sec^2, butterfly,
Using reference angles to evaluate: first, locate the? Then, you must? Ex. Anything with a denominator of 3 will have the values? The only things that change are the? The correct Reference angle is between the?(2) for an angle ex. tan (-210 degrees), what do you do? (3) For csc (11pie/4,) what do you do? (2) arc length equation? s is the?
Quadrant, solve, (1/2, √3/2), signs, x axis/angle, find the quadrant/find the angle values/apply tangent equation y/x, solve for the sin value/apply 1/sin = csc, S = r • theta, arc length,
For tan 1/0, the answer is? When converting from degrees to radians, write pie/3 as pie/3. Don't write: "pie/3 radians." length of terminal side equation? Sin equation? Cos? Tan? Cot? Sec? Csc? Pie/6. How do you find it in quadrant 2? Quadrant 3? 4? Cos 0? Sin 0? Remember: given angle sin 3pie/2. Find the? Then identify the? For 15pie/2: count by odd? (For the pie/2 values).
Undefined,r = square root of x^2 + y^2, sin = y/r, cos = x/r, tan = y/x, cot = x/y, sec = r/x, csc = r/y, pie - angle, pie + angle, 2pie - angle, 1, 0, graph values, sine y portion, numbers,
Right triangle equations: cos, sin, and tan? 45-45-90 triangle? 30-60-90 triangle? How do you evaluate whether angles are coterminal? Problem: Find the coterminal angle between 0 and 2pie. The answer should be in? To find a positive and negative coterminal angle for an angle, add or subtract by? If the angle moves clockwise, the sign will be?
adjacent/hypotenuse, opposite/hypotenuse, opposite/adjacent, x = 45/ x = 45/ x square root of 2 = 90, x = 30/ 2x = 90 / x square root of 3 = 60,add or subtract 2pie to see if the values overlap, radians, 2pie, negative,
Trig functions of any angle: equations? (6) Function opposite pairs? (3) to find values: ex. Sin theta = -3/5 and tan theta <0. What do you do? (3)
cos t =x / sin t = y/ tan t = y/x/ csc t = 1/y or sin sec t = 1/x or cos / cot t = x/y or 1/tan, cos and sec / sin and csc/ tan and cot, identify the quadrant/draw a triangle/solve for all values,
Trig identities: sin theta? Csc theta? Cos theta? sec theta? Tan theta? (2) Cot theta?(2) Pythagorean identities? (3)
sin = 1/csc, csc = 1/sin, cos = 1/sec, sec = 1/cos, Tan = 1/cot or sin/cos, cot = 1/tan or cos/sin theta, cos^2 + sin^2 = 1/ 1 + tan^2 = sec^2/ 1+ cot^2 = csc^2