Trigonometry Learning Strategies What should students be able to do within this interactive? Identify a right triangle. Identify the acute reference angles. Recognize and name the sides, and hypotenuse from a given reference angle. Recognize the ratios defining sine, cosine and tangent. Select the appropriate trigonometric ratio required to solve for the unknown. Recognize the substitution of the sides and/or angle into the trigonometric ratio. Understand the mathematical calculations required to solve for the unknown. Common mistakes made by students: Not being able to name the, or hypotenuse from a given reference angle. Not choosing the proper trigonometric ratio based on the information given. Not substituting the given information correctly into the ratio. Not using the correct mathematics to solve for the unknown. Curriculum Connections: Please note all of the following correlations match outcomes in the new Mathematics Kindergarten to Grade 9 Program of Studies (2007). 10-C Measurement SO4: Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. 10-3 Geometry SO4: Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by: applying similarity to right triangles generalizing patterns from similar right triangles applying the primary trigonometric ratios solving problems. 10-3 Algebra SO1: Solve problems that require the manipulation and application of formulas related to: perimeter area the Pythagorean theorem primary trigonometric ratios income. Junior High Math Interactives Page 1 of 6
Print Activity notes: *Note: The Print Activity is not intended to be an assessment piece. It is necessary for students use the Explore It mode to work through the Print Activity. Students will be asked to select a trigonometric function, an unknown and a reference angle to work from. The diagram may be altered by dragging one or both of the acute angles. The known values are substituted into the selected ratio and the mathematical calculations are performed in order to solve for the unknown. The print activity will allow students to identify the effects of making their selections. The Print Activity may be opened in Word Format instead of PDF so that changes to questions can be made. Trigonometry Print Activity Key Use the Explore It mode to answer the following questions: 1. State the names of the 3 trigonometric ratios that are listed under the Function section of the screen: sin R, cos R, tan R. 2. a. R and S are referred to as reference angles. b. T in the diagram, is called a right or 90 angle. 3. Select and answer the following questions: a. The Function is sin R. (sin R, cos R, tan R) b. The Unknown is. c. The Reference Angle is R_. d. On the diagram, side SR is _18.03 cm, R = _45_, and T = _45_. e. Sin R is defined as the ratio: hypotenuse f. The length of the hypotenuse is _18.03_ cm. g. As a decimal, sin 45 is equal to 0.707_. h. The result for the length of the unknown side is _12.8_ cm. Junior High Math Interactives Page 2 of 6
4. To answer the following questions select: Function: cos a. The Unknown automatically changed to the side. b. The ratio for cos S is: hypotenuse c. The result of the length of the side is _12.8_ cm. 5. To answer the following questions select: Function: tan Unknown: Opposite Drag vertex R on the diagram until S becomes 55. a. The ratio for tan S is: b. As a decimal, tan 55 is equal to _1.427_. c. The length of the side is 12.8 cm. d. The result for the length of the unknown side is _18.2_cm. 6. To answer the following questions select: Function: sin Unknown: Hypotenuse Drag vertex R on the diagram until S becomes 61. a. The ratio for sin S = hypotenuse Junior High Math Interactives Page 3 of 6
b. hypotenuse = c. hypotenuse = 23cm sin 61 23cm 0.875 d. The result for the length of the hypotenuse is _26.3_cm. 7. To answer the following questions select: Function: cos Unknown: Adjacent Drag vertex S on the diagram until it becomes 35. Click on corner. twice to place the diagram in the top right a. cos S hypotenuse b. cos 35 = 22.22 c. = cos 35 (0.819) 22.22 d. The result for the length of the side is _18.20 cm. 8. To answer these questions select: Function: tan Unknown: Opposite Reference Angle: R Drag vertex R on the diagram until it becomes 53. Click on right corner. three times to place the diagram in the bottom a. tan 53 = 9.6cm Junior High Math Interactives Page 4 of 6
b. The result for the length of the side is _12.8_cm. 9. To answer these questions select: Function: cos Unknown: Angle R a. The Reference Angle must be R. b. cos R = 12.8cm 18.03cm c. The result for the size of the unknown angle is 45. d. Move the scale slider to 1.5. cos R = 19.2cm 27.05cm e. The result for the size of the unknown angle is 45. f. Move the scale slider to 2. cos R = 25.5cm 36.06cm g. The result for the size of the unknown angle is 45. h. Changing the scale of the diagram does not change the measure of the _angles_ of the diagram (sides/angles) but does change the _sides. (sides/angles) Junior High Math Interactives Page 5 of 6
10. a. In the diagram below, use A as the Reference Angle to fill in the boxes with the correct description of the sides: Opposite, Adjacent or Hypotenuse. B Hypotenuse Opposite A Adjacent C Use the diagram above to complete the following ratios. Choose the appropriate names for the sides: b. sin A = hypotenuse c. cos A = hypotenuse d. tan A = Junior High Math Interactives Page 6 of 6