PPT-Right Triangle Trig Applications

Angles of Elevation and Depression Dr Shildneck Fall 2014 Tips for Solving Word Problems Draw a picture And fill in what you know Find the right triangles in the picture that you will need to use. Given circle of radius . r. , a radian is the measure of a central angle subtended by an arc length . s. equal to r. . The radian measure of an arbitrary angle. There are radians in a angle. Why? . Now take the same triangle and put a circle around it. The origin of the circle is at the lower left hand corner of the triangle. The radius of the circle is the length of the hypotenuse. The or Mathematics Course Additions. December 2011. What are the . current . offerings for 4. th. year math students at the High School?. Reasons for current courses. :. 3 credits were required in the past in mathematics to graduate. Verifying trig identities algebraically involves . transforming one side . of the equation into the same form as the other side using basic trig identities and properties of algebra. . Procedure for Verifying Trig Identities. Introduction- . Finding lengths. Sin, cos or tan to find lengths?. Finding missing lengths worksheet. Finding the Area of Triangles and Segments. The Sine rule. The Cosine Rule. The Sine and Cosine Rule (quiz and worksheet). (RIGHT TRIANGLES). Why do we Need Trigonometry?. In Physics, we will often be using right triangles in diagrams. Trigonometry lets us find missing side lengths and angles of right triangles.. Is it . Verifying trig identities algebraically involves . transforming one side . of the equation into the same form as the other side using basic trig identities and properties of algebra. . Procedure for Verifying Trig Identities. Definition of Inverse Trig Functions. Graphs of inverse functions. Page 381. Ex. 1 Evaluating Inverse Trig Functions. a). arcsin. (-1/2). b). arcsin. (0.3). Properties of Inverse Functions. If -1≤x≤1 and –. Some needed trig identities:. Trig Derivatives. Graph . y. 1. = sin x. . and . y. 2. = . nderiv. (sin x). What do you notice?. Proof Algebraically. (use trig identity for . sin(x + h). ). Proof Algebraically. We have already discussed a few example of trig identities. All identities are meant to serve as examples of equality. Convert one expression into another. Can be used to verify relationships or simplify expressions in terms of a single trig function or similar. x. .. Sketch the graph of g(x) = . ln. x.. If f(x) = 2. x. , then explain the transformation of f(x) = 2. x 3. 5.. Convert to radian measure:. 150. 0. , 225. 0. , 300. 0. , -60. 0. .. Convert to degree measure:. Use the triangle given to find the following trig ratios. sin( θ ) cos ( θ ) tan( θ ) Solve for x in the proportions below. 5.   Warm Up 1/20 Get out a colored pen and last night’s homework Right Triangle Trigonometry. Essential Question – How can right triangles help solve real world applications?. The Pythagorean theorem. In a rt . Δ. the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.. 2. Today’s Objective. Review right triangle trigonometry from Geometry and expand it to all the trigonometric functions . Begin learning some of the Trigonometric identities. What You Should Learn.