PPT-Graph Tangent, Cotangent, Secant and Cosecant

Objective Students will be able to graph and identify the basic trig functions and their graphs with transformations Tangent basic graph is the same as sin and cosine. Learning Goals:. Graphs of the Cosecant, Secant, and Cotangent Functions. Graph transformations . When you think about the . csc. , sec, and cot graphs what do you think about?. Graph of the Cosecant Function. Tangent Lines. Average Rate of Change. The . average rate of change. of a quantity over a period of time is the slope on that interval of time.. Ex.:. . Find the average rate of change of . f(x) = x. Secant and Tangent. Interior angle = ½ intercepted arc. Two Secants:. Interior angle = ½ (sum of intercepted arcs). Two Secants. Exterior angle = ½ (far arc – close arc). Two Tangents. Exterior angle = ½ (far arc – close arc). RULE 1. If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other. Explanation for Rule 1:. Intersecting Chords Rule:. Find the equations of tangents at given points. Find the points on the curve if tangent slope is known. Find equations of tangents . parallel. to given lines through a given point.. Find equations of tangents . Differentiability. Local Linearity. Local linearity is the idea that if we look at any point on a smooth curve closely enough, it will look like a straight line. Thus the slope of the curve at that point is the same as the slope of the tangent line at that point. Segments and Lines in relation to circles. Review of Terms and Ideas. Tangent. Line or segment that touches a circle at one point ( point of tangency). This line or segment is perpendicular to the radius at this point. Goals for today:. Graph sine, cosine and tangent graphs by hand. Identify areas of increase/decrease/positive/negative on graphs of trig functions. Accurately identify amplitude and midline of a trigonometric graph or function. NOW: . Replace: . Graph of . , with words:. Graph: (. , the . slope of the tangent line to the . function . . at that . point). .  . CALCULUS problem:. Graph: (. , the slope of the tangent line to the function . Function Review.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 2.1 – . Rates. of Change and Tangents to Curves. Function Review.  .  .  .  .  .  . 2.1 – . Rates. of Change and Tangents to Curves. . . as .  . Secant Line and Tangent Line. Slope of secant line . Slope of tangent line as .  . is.  . the derivative of . at . t. he instantaneous rate of change of . at . Year 12 pupils i.biza@uea.ac.uk This study focuses on a teaching experiment applied in a Year 12 class for the introduction of the derivative and the tangent line of function graph. This experiment was based on re The set of all points in a plane that are equidistant An angle whose vertex is the is 15 16 A radius drawn to a tangent at the point of 17 exterior point to a circle are congruent 18 In