Applications of trigonometric functions, how are trigonometric functions applied?

It is impossible to get a fixed triangle by knowing only one corner and one side, and only by knowing three sides or two corners can a triangle be established, and then it can be solved by the cosine theorem or the sine theorem. Trigonometric functions are generally used to calculate the edges of unknown lengths and unknown angles in triangles, and have a wide range of uses in navigation, engineering, and physics.

For example, if the interface at the right-angle elbow is made of two iron sheets and connected vertically with two trees, then the tangent line at the interface of the iron sheet is part of it, and only in this way can the splicing thickness be guaranteed to be vertically connected.

The primary phase represents the starting position, i.e., t=0

The actual distance can not be found, the maximum distance from the single pendulum to both sides is 6, but the two highest points and the equilibrium position are not in the same horizontal line, so the actual horizontal distance can not be added, and the length of the single pendulum must be known. Then the horizontal distance y is.

y= l, less than 12

Did you start studying high school physics? In the first lesson on pendulums, we had this experiment.

Phase 6, as the name suggests, is the position of the initial swing of the single pendulum"The horizontal distance between the highest point on one side and the highest point on the other"In fact, it is equal to the vertical distance between the peak and trough of s=6sin(2 t+6). That is, 12.

If you can't understand it, you can check out the hourglass experiment of the single pendulum in high school physics.

The two highest points should be on the same level! ~

Trigonometric functions are used in a wide range of applications, such as:

Parking lot design issues.

Analysis: The area of the rectangle is related to the position of point P, connect AP, and extend RP to AB at M. If rp=x is directly set, although some expressions of related line segments can be obtained in the future, the maximum value of this method to solve the area is very complex, and the trigonometric function is used here, which will be much faster.

Let pab=seta, then the line segments PM, AM, PR, and pq can be represented, and then the area can be represented by a trigonometric function in the macro calendar. Next, further simplification, you can get the best value of the year's spine.

2.Calculate the height, distance problem (this is the most common).

Analysis: This rocket launch problem is a typical example problem, and the solution method is very simple, so I don't need to do much analysis.

Your question is not very good, if you know that a certain corner and an edge cannot be found in all the edges.

But according to what you mean, I will give you 2 formulas to look at, these 2 formulas can explain the relationship between the corners of triangles very well.

1.Sine theorem: a sina = b sinb = c sinc, you can use it to find unknown edges or angles.

2.Triangle area = absinc, this formula can relate the corner edges to the area of the triangle.

ps: To supplement your mistake, the trigonometric formula is not built in a Cartesian triangle, but in a Cartesian coordinate system, the sine value of the triangle = y r (in the unit circle), which is the knowledge in high school compulsory 4, and it is not necessary to master it in junior high school.

Reciprocal relation: cot *tan = 1

Quotient relationship: sin cos = tan

Square relationship: sin +cos = 1

Sine theorem: In ABC, a sin a = b sin b = c sin c c = 2r

where r is the radius of the circumscribed circle of abc.

Cosine theorem: In ABC, B2 = A2 + C2 - 2AC·COS.

where is the angle between edge a and edge c.

Induction formula for trigonometric functions (six formulas).

Equation 1: Let any angle, and the value of the same trigonometric function for the same angle with the same terminal edge be equal:

sin( +k*2 )=sin (k is an integer) cos( +k*2 )=cos (k is an integer) tan( +k*2 )=tan (k is an integer) Equation 2 is set to be an arbitrary angle, the relationship between the trigonometric value of + and the trigonometric value of

sin[(2k+1)π+=-sinα

cos[(2k+1)π+=-cosα

tan[(2k+1)π+=tanα

cot[(2k+1)π+=cotα

The relationship between the trigonometric value of the equation three arbitrary angles and -

sin(2k-α)=-sinα

cos(2k-α)=cosα

tan(2k-α)=-tanα

cot(2k-α)=-cotα

Equation 4 uses Equation 2 and Equation 3 to get the relationship between - and the trigonometric value of

sin[(2k+1)π-=sinα

cos[(2k+1)π-=-cosα

tan[(2k+1)π-=-tanα

cot[(2k+1)π-=-cotα

Equation 5: Using Equation 1 and Equation 3, we can get the relationship between the trigonometric values of 2 - and

sin(2kπ-α=-sinα

cos(2kπ-α=cosα

tan(2kπ-α=-tanα

cot(2kπ-α=-cotα

Equation 6: The relationship between 2 and the trigonometric value of

sin(π/2+α)=cosα

cos(π/2+α)=-sinα

tan(π/2+α)=-cotα

cot(π/2+α)=-tanα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

tan(π/2-α)=cotα

cot(π/2-α)=tanα

Induction formula Memorize the trick: odd and even unchanged, and the sign looks at the quadrant. [2] Or it can be noted: the division is integer, and the sign is seen in the quadrant.

Equal to 3 10

If tan is given in the question, you can use the two core formulas of tan sin cos and sin square cos square 1.

Trigonometric function is a major branch of function, which has its applications in physics, mechanics, and navigation.

1.Trigonometric functions can be used for the frequencies and periods of sound waves, light waves, short waves, and various waves.

2.The heart beat frequency is also related to the use of trigonometric functions.

3.The elevation of the tide can also be expressed by the trigonometric formula: y=asinwx+k.

Measure the height of a shadow object

Combined with angle of view questions

Substitution is 1=sin2a+cos2a (2 is squared).