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Applications of Trigonometric Functions

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Presentation on theme: "Applications of Trigonometric Functions"— Presentation transcript:

1 Applications of Trigonometric Functions
Unit 4 Applications of Trigonometric Functions

2 Learning Goal/ Big Idea
Learning Goal: Students will apply the derivatives of Sinusoidal functions into real life problems Big Idea: The same algebraic expression or equation can be related to different real-world situations, and different algebraic expressions or equations can describe the same real-world situations.

3 Minds On Why derivatives of a sinusoidal function?

4 Review

5

6 Applications of Sinusoidal Functions
A power supply delivers a voltage signal that consists of an alternating current (AC) component and a direct current (DC) component. Where t is the time, in seconds, the voltage, in volts, at time t is given by the function V(t)=5sint+12 a) Find the maximum and minimum voltages. At which times do these values occur? b) Determine the period, T, in seconds, frequency, f, in hertz, and amplitude, A, in volts, for this signal

7 2. A piston in an engine oscillates up and down from a rest position
2. A piston in an engine oscillates up and down from a rest position. The motion of the piston can be approximated by the function h(t)=0.05cos(13t), where t is time, in seconds, and h is the displacement of the piston head from rest position, in meters, at time t. A) Determine an equation for the velocity of the piston head as a function of time B) Find the maximum and minimum velocities and the times at which they Occur.

8 3. A pendulum has a length of 50cm and a maximum horizontal displacement of 8cm.

9 3. A pendulum has a length of 50cm and a maximum horizontal displacement of 8cm.
C) Determine a function that gives the velocity of the bob as a function of time. D) Determine a function that gives the acceleration of the bob as a function of time.

10 3. A pendulum has a length of 50cm and a maximum horizontal displacement of 8cm.
E) Find the maximum velocity of the bob and when it occurs.

11 3. A pendulum has a length of 50cm and a maximum horizontal displacement of 8cm.
F) Find the maximum acceleration of the bob and when it first occurs.

12 3. A pendulum has a length of 50cm and a maximum horizontal displacement of 8cm.
G) Determine the times at which i) the displacement equals zero ii) the velocity equals zero iii) the acceleration equals zero

13 Exit Ticket Find the derivative of f(x)= cotx


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