Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name______________________________________ Geometry Period_____ 9-7 Notes Date_________ Lesson 9-7: Re-writing Trigonometric Expressions-Cofunctions Todayβs Aim: How can we use relationships within right triangles to help us re-write Trigonometric ratios? Letβs Re-activate our knowledge What do we call these different parts of a trig function? The _____________ ( function. ) of the trig The ______________ or ______________ of the trig function. Often, mathematicians will use Greek letters to identify an angle in a right triangle. Theta Try writing some here: ______ Gamma Try writing some here: _______________ Group Exploration READ and answer the following questions in your groups: 1. What type of triangle is shown here? How do you know? 2. Using your answer from Question # 1 and your knowledge of the interior angles of triangles, what MUST be the sum of π πππ πΎ ? Therefore the two non-right angles in a right triangle must always be 3. Write the indicated trig ratios using the sides of the triangle shown above : πΆππ π= πππ πΎ = 4. What do you notice about these values? a) Will this be true for ALL right triangles? Try another ( Triangle ABC) πΆππ π₯ = πππ π¦ = . Letβs summarize as a class: The VALUE of sine of an acute angle is equal to the _ complement. Symbols: of its Example: The VALUE of cosine of an acute angle is equal to the complement. Symbols: of its Example: We call Sine and Cosine . Letβs try! 1. Write each expression as a function of an acute angle. a. sin 80Λ b. cos 36Λ 2. Each equation contains the measures of two acute angles. Find a value of ΞΈ for which the statement is true. Remember! In cofunctions, VALUES are equal and ANGLES are complements. 1) sin 10° = cos ΞΈ 2) sin ΞΈ = cos 2ΞΈ 3. In right triangle ABC with the right angle at C, sin A = 2x + 0.1 and cos B = 4x β 0.7. Determine and state the value of x. Explain your answer. Youβre Turn! 4) Write the expression in terms of sine and/or cosine. A) sin 7ο° B) cos 31ο° 5) Which ratios are equal to ½? Select all that apply: a. sinL b. cosL c. sinJ d. cosJ 6) Write sin(30°) in terms of its co-function. π₯ π₯ 7) Math-Hoo uses the equation sin49 = 16 to find BC. His cousin Hal uses the equation cos41 = 16 to find BC. Who is correct? Explain. Fill it in! 8) 7) In , the complement of is . Which statement is always true? 1) 2) 3) 4) 8) In right triangle ABC with the right angle at C, sin A = 2x + 5 and cos B = 4x β 15. Solve for x. Explain your solution. Name_____________________________________ Geometry Period______ 9-7 HW Date_________ 1) Find sin J, sin K, cos J, and cos K. Write each answer as a ratio. 2) Write the expression in terms of sine or cosine. a) sin 22ο° = cos ________ b) cos 56ο° c) cos 15ο° 3) Find the value of x and y. Round to the nearest tenth. 4) The angle of depression is 11ο° from the bottom of a boat to a deep sea diver at a depth of 120 feet. Find the distance x the diver must swim up to the boat to the nearest foot. 5) In , where is a right angle, 6) Find the value of R that will make the equation . What is ? true when . Explain your answer. 7) In right triangle ABC with the right angle at C, sin A = 3x + 5 and cos B = x β40. Solve for x.