360 - A Quadrantal 0, 90, 180, 270 - terminal side is on axis - no reference triangle - 2 undefined values Quadrants Signs Positive when ASTC - All, Sin, Tan, Cos Range of sin -1 <= sin () <= 1 Range of cos -1 <= cos () <= 1 ...
In the next image, we show the four quadrants and the coordinate axes. Four quadrants and labeled coordinate axes Let's see a couple of unit circle triangles in a figure because they will help us when defining the trigonometric functions. Unit circle, points P and Q and right triangles ...
In the case of the trig functions, the graph is pretty easy to draw if you look at the unit circle for a while. The strategy is simple: start out at q=0o, and follow the unit circle around, watching what the y-coordinate does (for the sine, that is; watch the x-coordinate for...
The trouble is that Arctan yields values in (−π/2, +π/2), which is Quadrants IV and I. But the cosine is always positive on that interval. Therefore cos(Arctan x) always yields a positive result. Remember also from equation 22 that cos(−A) = cos A. To ensure this, use ...
Find the exact values of each of the 6 trigonometric functions of an angle θ if (4, -3) is a point on its terminal side in standard position. (-∞,∞), [-1, 1], (-∞,∞), [-1, 1], x doesn't equal odd multiples of π/2, (-∞,∞), x doesn't equal multiples of π...
Answer to: Answer true or false: There are only two essential trig functions (all other trig functions can be defined in terms of those two). By...
Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is:The point (12,5) is 12 units along, and 5 units up.Four QuadrantsWhen we include negative values, the x and y axes divide the space up into 4 pieces:Quadrants I, II, III and IV...
The Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the x-axis and the y-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant; the quadrants are number...
We would simply replace sec y with x, and take the positive root of tan y, because tan y is positive in the first and third quadrants. In the graph of y = arcsec x with that range, the slope for negative x is negative. The disadvantage of taking that range is that, when x is ...