Trigonometry Intro: The RatiosName: ______

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Launch the “Sine, Cosine, and Tangent” gizmo. If the Gizmo doesn’t open automatically, right-click it & chose “run this plug-in” … you might need to update the Flash.

The Sine Ratio

  1. In the Gizmotm, on theSINEtab, setmAto 30.
    (To quickly set a value, type a number in the box to the right of the slider and pressEnter.) NoticeABC.
  2. Which angle has degree measure 30? ______
    Which angle is the right angle? ______
    What ismB? ______
  3. Which side is the hypotenuse? ______
    How do you know that? ______
    Which leg ofABCis oppositeA? ______
  4. Click onClick to measure lengthsto turn on the Gizmo rulers.
    (For help using the rulers, click onGizmo help,below the Gizmo.)
  5. Use the rulers to measure the length of the side oppositeAand the length of the hypotenuse. If these two lengths are not whole numbers, drag pointCuntil they are. (Be suremAis still 30°.)
    What are the side lengths? ______
    Click onShow side lengthsto check your work.
  6. In a right triangle, the ratio of the length of the leg opposite an angle to the length of the hypotenuse is called thesineof the angle. (You can remember this as, "Sine equals opposite over hypotenuse.") The sine ratio is abbreviatedsin.

    What is sin 30°? Write your answer as a fraction. ______
    Simplify the fraction and write it as a decimal: ______
    Click onShow sine computationto check your answer.
  7. Change the size ofABCby draggingC, keepingmA=30°.
    What is always true about sin 30°? ______
    ______
    ______

The Cosine Ratio

  1. Click on theCOSINEtab.
    Turn offShow side lengthsandShow cosine computation.
    SetmAto 50°.
  2. Which angle has degree measure 50? ______
    Which angle is the right angle? ______
    What ismB?______
  3. Which leg ofABCis adjacent toA? ______
    Which leg ofABCis adjacent toB? ______
    Which side is the hypotenuse?______
  4. Turn on the Gizmo rulers.
  5. Use the rulers to measure the length of the side adjacent toAand the hypotenuse. What are those lengths? ______
    Click onShow side lengthsto check your work.
  6. In a right triangle, the ratio of the length of the leg adjacent to an angle to the length of the hypotenuse is called thecosineof the angle. (You can remember this as, "Cosine equals adjacent over hypotenuse.") The cosine ratio is abbreviatedcos.

    What is cos 50°? Write your answer as a fraction : ______.
    Then use a calculator to approximate this fraction as a decimal. Round your answer to three decimal places. ______.
    Click onShow cosine computationto check your answer.
  7. Change the size ofABCby draggingC, keepingmA=50°.
    What is always true about cos 50°? ______
    ______
    ______
  8. Using the same triangle, find sin 40°.
    First write it as a fraction, ______
    then as a decimal, rounded to three decimal places______Compare sin 40°= ______to cos 50° = ______.
    What do you notice? ______
    Find another pair of angles for which this is true. ______

The Tangent Ratio

  1. Click on theTANGENTtab. SetmAto 25°.
  2. Which leg ofABCis oppositeA? ______
    Which leg ofABCis adjacent toA? ______
    Which side is the hypotenuse?______
  3. Which leg ofABCis oppositeB? ______
    Which leg ofABCis adjacent toB?______
  4. Turn on the Gizmo rulers.
  5. Use the rulers to measure the length of the leg oppositeAand the length of the leg adjacent toA.
    What are those lengths? ______
    Click onShow side lengthsto check your work.
  6. In a right triangle, the ratio of the length of the leg opposite an angle to the length of the leg adjacent to an angle is called thetangentof the angle. (You can remember this as, "Tangent equals opposite over adjacent.") The tangent ratio is abbreviatedtan.

    What is tan 25°? Write your answer as a fraction, ______
    then as a decimal, rounded to three decimal places. ______
    Click onShow tangent computationto check your answer.
  7. Change the size ofABCby draggingC, keepingmA=25°.
    What is always true about tan 25°? ______
    ______
  1. Turn off the rulers, turn offShow side lengthsandturn off Show tangent computation.
    Use what you have learned about the tangent ratio to answer these questions.
  2. What is tan 45°? ______
    Explain why your answer makes sense. ______
    ______
  3. InABC, withCthe right angle, if tanA=, what is tanB? ______
    Explain your answer. ______
    ______
    Provide a sketch of this triangle to support your answer:

Practice: khanacademy

Trigonometry 0.5:

Trigonometry 1: