![]() ![]() If we take point R, we take six units to the left, one, two, three, four, five, six, seven up, one, two, three, four, five, six, seven. It'll put it right over there, so that is point P. So if we take point P, six to the left, one, two, three, four, five, six, seven units up, one, two, three, four, five, six, seven. So each of these points are going to go six units to the left and seven up. Then a translation six units to the left and seven units up. And so after you do the 90-degree rotation, PQR is going to look like this. It's going to, once again, also do a 90-degree rotation about R. And then Q is going to go right over here. So P is going to be there and you can see that. Now when you do the rotation, you're going to go to the right one and then up three. One way to think about it is to go from R to P, we went down one and three to the right. But P is now going to be right over here. So if we rotate this 90 degrees, so one way to think about it is, a line like that is then going to be like that. And then we'll do the rest of this sequence. So first it says a rotation 90 degrees about the point, about the point R, so let's do that. ![]() So remember, we're starting with triangle PQR. So let's first think about Sequence A, and I will do Sequence A in this purple color. So pause this video and have a go at that. Which of the following sequences of transformations maps triangle PQR onto triangle ABC? So we have four different sequences of transformations, and so why don't you pause this video and figure out which of these actually does map triangle PQR, so this is PQR, onto ABC, and it could be more than one of these. The side length of each square on the grid is one unit. Some prefer to do all the transformations with t -charts like we did earlier, and some prefer it without t -charts (see here for the sine and cosine transformations specifically, and here for help with all the trig functions).We're told that triangles, let's see, we have triangle PQR and triangle ABC are congruent. Later we’ll be transforming the Inverse Trig Functions here. Now we will transform the six Trigonometric Functions. We learned how to transform Basic Parent Functions in the Parent Functions and Transformations section. Transformations of all Trig Functions without T-Charts Writing Equations from Transformed Graphs for Sin and Cos Writing Equations from Transformed Graphs for Sec, Csc, Tan, and Cot T-Charts for the Six Trigonometric Functions Applications of Integration: Area and Volume.Exponential and Logarithmic Integration.Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation. ![]() Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Conics: Part 2: Ellipses and Hyperbolas.Graphing and Finding Roots of Polynomial Functions.Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even/Odd, Extrema.Solving Radical Equations and Inequalities. ![]() Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.Algebraic Functions, including Domain and Range.Systems of Linear Equations and Word Problems.Introduction to the Graphing Display Calculator (GDC).Direct, Inverse, Joint and Combined Variation.Coordinate System, Graphing Lines, Inequalities.Types of Numbers and Algebraic Properties.Introduction to Statistics and Probability.Powers, Exponents, Radicals, Scientific Notation. ![]()
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