"Applications of Trigonometric Functions" Trigonometric Functions PPT Courseware

Description

"Applications of Trigonometric Functions" Trigonometric Functions PPT Courseware

Part One: Learning Objectives

Understand that trigonometric functions are important function models that describe periodic change phenomena.

Ability to use trigonometric function models to solve simple practical problems

Application of trigonometric functions PPT, part 2: independent learning

Problem guide

Preview textbooks P242-P248 and think about the following questions:

1. In simple harmonic motion, what are the initial phase, amplitude and period of y=Asin(ωx+φ)?

2. What are the four steps to solve trigonometric function word problems?

A preliminary exploration of new knowledge

1. The physical meaning of the parameters in function y=Asin(ωx+φ), A>0, ω>0

■Instructions from famous teachers

When A<0 or ω<0, you should first use the induction formula to convert the coefficient of x or the number before the sign of the trigonometric function into a positive number, and then determine the initial phase φ. For example, the initial phase of the function y=-sin2x-π4 is not φ =-π4.

2. Trigonometric function model building procedure

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) Function y=Asin(ωx+φ), the maximum value of x∈R is A.()

(2) The initial phase of the function y=Asin(ωx-φ) is φ.()

(3) When the "five-point method" is used to draw a simple diagram of the function y=2sinx+π3 on a period, the first point is π3, 0.()

The period and amplitude of the function y=2sinx2+π5 are ()

A． 4π,-2B. 4π,2

C． π,2D． π,-2

The graph of function y=Asin(ωx+φ)+k is as shown in the figure, then its amplitude A and minimum positive period T are respectively ()

A． A=3, T=5π6 B. A=3, T=5π3

C． A=32, T=5π6 D. A=32, T=5π3

It is known that someone's blood pressure satisfies the functional analytical formula f(t)=24sin(160πt)+115. Where f(t) is the blood pressure (unit: mmHg), t is the time (unit: min), then the person's heartbeat per minute The number of times (the number of heartbeats is the frequency) is ()

A． 60 b． 70

C． 80 D. 90

It is known that the relationship between the change of current intensity I (A) and time t (s) is I=5sin100πt+π3, then when t=1200s, the current intensity is ()

A． 5A B. 2.5A

C． 2A D. -5A

Application of trigonometric functions PPT, the third part: interactive teaching and practice

Applications of trigonometric functions in physics

It is known that a small ball hung by a spring vibrates up and down. The functional relationship between its distance h (cm) from the equilibrium position (position at rest) and time t (s) is h=3sin2t+π4.

(1) Find the position where the ball starts to vibrate;

(2) Find the coordinates of the ball when it first rises to the highest point and drops to the lowest point.

Solving strategy

Strategies for using trigonometric functions to solve physics problems

(1) Physics problems often involved include pendulum, light wave, electric current, mechanical wave, etc. Their common feature is periodicity.

(2) Clarify the meaning of physical concepts. Such problems often involve concepts such as frequency, amplitude, etc., so you must be familiar with their meanings and combine them with the corresponding knowledge of trigonometric functions to solve problems.

Applications of trigonometric functions in real life

As shown in the figure, the radius of a water wheel is 4 m. The center O of the water wheel is 2 m away from the water surface. It is known that the water wheel rotates 5 times per minute. The time starts when point P on the water wheel emerges from the water (point P0 in the picture).

(1) Express the height z (m) of point P from the water surface as a function of time t (s);

(2) How long does it take for point P to reach the highest point for the first time?

Application of trigonometric functions PPT, Part 4: Feedback on achievement of standards

1. The flow of people in a mall is defined as the number of people passing through the entrance every minute. The flow of people in a mall on May Day satisfies the function F(t)=50+4sint2(t≥0). In which of the following time periods does the flow of people increase? ()

A． [0,5]B． [5,10]

C． [10,15] D. [15,20]

2. The functional relationship between the displacement y of a spring oscillator and time t is y=Asin(ωt+φ)(A>0,ω>0). If the amplitude of the spring oscillator’s motion is 3, the period is 2π7, and the initial phase is π6, then this The analytical formula of the function is _________.

3. The population of a certain animal is as low as 700 on January 1 and as high as 900 on July 1. Its total population changes according to a sinusoidal curve between these two values.

(1) Find the analytical formula of the function of population quantity y with respect to time t; (where t is based on the number of months that have passed since the beginning of the year as the unit of measurement)

(2) Draw a sketch of the change of population size y with respect to time t.

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"Applications of Trigonometric Functions" Trigonometric Functions PPT download:

"Applications of Trigonometric Functions" Trigonometric Function PPT Download Part One: Learning Objectives 1. Understand that trigonometric functions are important function models that describe periodic changing phenomena, and be able to use trigonometric function models to solve some simple practical problems. (Key points) 2. Practical questions...

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Update Time: 2024-09-08

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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