Solving trigonometric functions, how to solve trigonometric functions

Using sina + sinb = 2 sin((a+b) 2)cos((a-b) 2

sin(7c)-sin(5c)=sin(7c)+sin(-5c)=sinc

2sinc*cos(6c)=sinc

If Sinc = 0, then C = K + 2, K Z If Sinc is not zero, then Cos(6C) = 1 26C = 2K + 6, K Z

c=kπ/3+π/36,k∈z

How to solve trigonometric functions is described below:

In trigonometric functions, it is known for its many formulas The solution method is also more flexible, but it is not impossible to find, of course, it has its regularity, and its regularity can always be reflected in the college entrance examination in recent years

A flat approach.

The condition and conclusion of the problem are the form of the algebra and form of the sine and cosine of the same angle trigonometric function or the form of the sine and cosine product, and the algebraic sum can be considered to be squared, so that the sum and difference can be organically combined with the product, and the solution can be solved smoothly from the loss of the front limb

2. Power reduction method.

The problem of simplification of higher-order trigonometric functions is often solved by the square relationship and the power reduction of the doubling relation.

3. Angle method.

There are also evaluation problems that can be solved by observing the relationship between angles and properly constructing them to relate them to special angles and other angles

Fourth, the exchange method.

When solving composite function problems in trigonometric functions, it is important to grasp the characteristics and skillfully switch elements to simplify complex problems.

5. Discussion method.

When it comes to trigonometric problems with positive and negative trade-offs or arguments, it is often necessary to discuss trade-offs

6. Imagery.

When solving trigonometric problems, sometimes it is necessary to use images to better solve the corresponding problem

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Trigonometric functions can also be defined equivalently in terms of the lengths of various line segments related to the unit circle. Trigonometric functions play an important role in the study of the properties of geometric shapes such as triangles and circles, and are also a fundamental mathematical tool for the study of periodic phenomena. In mathematical analysis, trigonometric functions are also defined as the solutions of infinite series or specific differential equations.

Allow them to extend their value to any real value, even complex value. The trigonometric analytic formula is y=asin(x+)k. Trigonometric function is one of the basic elementary functions, which is a function with angle as the independent variable, and the angle corresponds to the coordinate of the intersection point of the terminal edge of any angle with the unit circle or its ratio as the dependent variable.

tan=sin/cos

then tan+1 tan=sin cos+cos sin=1 (sincos).

So since sin+cos=2(??

Squared to get 1+2sincos=4, that is, sincos= so it's 1, all of the above are, sin+cos can't =2, so there is no solution to this problem.

This question is wrong, the maximum value of sinx+cosx can only reach the root of 2, and cannot be equal to 2.

I would like to ask, is there only 3 under this root number or is there also a b?

I'll do it with only 3 (this one is simpler):

Multiply cosa into parentheses, and then move the item to get the root number 3*bcosa=c*cosa+a*cosc

According to the sinusoidal theorem, ABC is replaced with sinasinbsinc respectively, and the root number 3*sinb*sina=sinccosa+sina*cosc=sin(a+c)=sin(pai-b)=sinb, and the two sides are about sinb, and sina = (root number 3) 3 is obtained

According to the sinusoidal theorem, a sina = b sinb = c sinc=2r is divided by 2r on both sides of the above equation

(3sinb-sinc)cosa=sinacosc=>3sinbcosa=sin(a+c)=sinb=>cosa=1/3

This is an open-ended question that needs to be discussed in categories: (below) 1If it is known that the angle of the right-angled edge corresponds to 30°, then sin30° = right-angled edge hypotenuse, and in turn the hypotenuse is equal to the right-angled side sin30°

known right-angled edges).

Then you can also invert the formula, right-angled edge = sin30° * hypotenuse] 2If it is known that the angle between the right-angled edge and the hypotenuse is 30°, the same is true for cos30° = right-angled edge and conviviality, and vice versa = right-angled edge cos30°

The reverse is the same].

If you are looking for another right-angled edge, use tangent, the specific method is as above, you can try it yourself, learn to help yourself, don't rely on other people's answers, follow my method to deduce it yourself, I hope you learn and progress.

Know the opposite side of 30 degrees with a sinusoidal solution.

Know the adjacent side of 30 degrees and use cosine to solve.

We all know that there is an angle of 30 degrees, and there is a right-angled side, which is a special angle with both the sine and cosine theorem.

a/sina=b/sinb=c/sinc=2r

a2=b2+c2-2bccosa

y=sin(2x+ 3)--y=sin[2(x+ 6)]The right sen number shifts 6 to get y=sin[2(x+ 6- 6)]=sin2x, the abscissa becomes 1 2, the period of the function is smaller, w becomes larger (multiplied by 2) and the former spring knowledge becomes huixiao y=sin4x

The axis of symmetry of sinx is the most worthwhile time.

So x=k + 2

4x=kπ+π2

k=0, so the axis of symmetry is x= 8

tanα/（tanα-1）=-1

tanα=1/2

The original formula is divided by cos 2

sin^2 α+sin αcosα+2=cosα^2（tanα^2+tanα）+2=3/4cosα^2+2

cos 2 = 1 (tan 2 + 1) = 4 5 so the original formula = 3 4 * 4 5 + 2 = 13 5

<> you refer to let the chaotic mu look at the accompanying auspiciousness! Tansen.

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