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Trigonometric Functions · Ages 16–17

Finding Amplitude and Period of Sine and Cosine

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For 11th-grade students. State the amplitude and period for each given function. Express periods in exact radian form.

  1. Find the amplitude and period of y = 3 sin(x).

  2. Find the amplitude and period of y = cos(4x).

  3. Find the amplitude and period of y = -5 sin(2x).

  4. Find the amplitude and period of y = 0.5 cos(x/3).

  5. Find the amplitude and period of y = -2 sin(πx) + 4.

  6. A cosine wave has a maximum value of 7 and a minimum value of -1, completing one cycle every 4 radians. Write its amplitude and period.

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Finding Amplitude and Period of Sine and Cosine

Answer key

  1. Find the amplitude and period of y = 3 sin(x).

    Amplitude: 3; Period: 2π

  2. Find the amplitude and period of y = cos(4x).

    Amplitude: 1; Period: π/2

  3. Find the amplitude and period of y = -5 sin(2x).

    Amplitude: 5; Period: π

  4. Find the amplitude and period of y = 0.5 cos(x/3).

    Amplitude: 0.5 (or 1/2); Period: 6π

  5. Find the amplitude and period of y = -2 sin(πx) + 4.

    Amplitude: 2; Period: 2

  6. A cosine wave has a maximum value of 7 and a minimum value of -1, completing one cycle every 4 radians. Write its amplitude and period.

    Amplitude: 4; Period: 4