What are the methods and techniques for solving trigonometric equations

Geometry only knows the sum difference of trigonometric functions, the sum of differences, and so on.

It is generally solved into familiar sine, cosine, and tangent equations, and sometimes has to be expressed by inverse trigonometric functions.

1. Solving equations; 2. Discussion method of dividing the struggling theory; 3. Translational coordinate axis method.

1. The so-called method of solving equations is to substitute the known conditions into the analytical formula of the function to be determined, list the equations about the unknown parameters, solve the equations, and obtain the solution of the parameters, so as to determine the analytical formula of the trigonometric function. This method is called the method of solving the system of equations.

2. The so-called analysis and discussion method is to analyze and discuss the known conditions according to the known conditions, and find the period, initial phase, amplitude, etc. of the function in turn, so as to determine the analytical formula of the trigonometric function. This method is called the taxonomic discussion method.

3. The origin is moved to the appropriate position by translating the coordinate axis through the line, so that it is easy to find the analytic formula of the function in the new coordinate system, but the method of reverting to the analytic formula of the function under the original coordinate system is called the translational coordinate axis method.

The two sides of the two types are respectively added to the royal clan to build the flat spike in the morning, and the town gets it.

80sinφ)^2 = 115^2

8864cosφ +80^2 = 115^28864cosφ =, cosφ =

64°56' +k · 360°

You only have one picture.,The 3-thirds of the pie on both sides is about to be dropped.,The left and right sides are multiplied by 2 at the same time.

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Questions. Solving the equation of trigonometric function process thank you.

Questioned? Questions.

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It is solved according to the periodicity of the trigonometric function:

Here: 2x=(2k+1) + 6 or 2k - 6 gives x=(k+7 12) or x=(k-1 12) k is any integer.

sin2x=2sin²x

2sinxcosx=2sin²x

sinxcosx=sin²x

sinx=0 or sinx=cosx

When sinx=0, x=0 or x=

When sinx=cosx, tanx=1, x=4, so x=0 or x= or x=4

It's a requirement to prove the above formula, right?

8sin^3 18°-4sin 18°

4sin18°(2sin²18°-1)

It can be known from the formula cos2a = 1 - 2 sin a that Wooki.

2sin²18°-1= -cos36°

Namely. 8sin^3 18°-4sin 18°-4sin18°×cos36°

Whereas. 4sin18°×cos36°

4sin18° cos36° cos18° cos18° can be known by the double angle formula, sin2a=2sina cosa, so. 4sin18°×cos36°×cos18°4sin18°×cos18°×cos36°2sin36°×cos36°

sin72°

Thereupon. 8sin^3 18°-4sin 18°-4sin18°×cos36°

4sin18°×cos36°×cos18° /cos18°-sin72° /cos18°

Obviously sin(90°-a) = cosa, i.e. sin72° = cos18°, so.

8sin^3 18°-4sin 18°

sin72° /cos18°

Namely. 8sin 3 18°-4sin 18°+1=0, the equation grinding orange talk is proven.