There is no simple notation for the induction formula of trigonometric functions

Yes, the mantra is: odd and even unchanged, and the symbol looks at the quadrant. Meaning:

Odd and even are contested for multiples of 90 degrees, such as: cos(180 degrees + a) = cos(2 * 90 degrees + a), 2 is the name of the even number unchanged, or cosa, the symbol sees the quadrant when a is regarded as an acute angle: 2*90 degrees + a in that quadrant to determine the symbol, because the terminal edge of 2*90 degrees + a is in the third quadrant, and the third quadrant has a negative cosine, so cos(180 degrees + a) = -cosa

This mantra is easy to use, try it, you will be satisfied, I won't lie to you, remember to give me extra points.

Yes. Suppose the terminal edge is an acute angle in the first quadrant. If you add , then the middle is in the third quadrant, so the y value is negative and the x value is negative, then both sin and cos are less than zero, so sin(a+)=-sina, cos(a+)=-cosa.

By analogy, it is assumed that a is an acute angle, so that the latter looks at the quadrants after the value is added, and then looks at the positive and negative of x and y to judge the positive and negative of sin and cos.

Trigonometric functions, just a few formulas.

It's a piece of cake for you.

In the high school entrance examination questions, trigonometric functions are not very difficult, it is relatively easy to get points, and the induction formula is the premise for solving trigonometric function problems, have you mastered them? Below I have sorted out the derivation process and memory methods of trigonometric function induction formulas for your reference!

What are the common induction formulas for trigonometric functions.

Let be any angle, and the value of the same trigonometric function for the same angle with the same end edge is equal:

sin(2kπ+αsinα (k∈z)

cos(2kπ+αcosα (k∈z)

tan(2kπ+αtanα (k∈z)

cot(2kπ+αcotα (k∈z)

Let be an arbitrary angle, the relationship between the trigonometric value of + and the trigonometric value of

sin(π+sinα

cos(π+cosα

tan(π+tanα

cot(π+cotα

The relationship between the trigonometric value of an arbitrary angle and -

sin(-αsinα

cos(-αcosα

tan(-αtanα

Trigonometric functions induce function memory formulas.

These induction formulas above can be summarized as:

For the trigonometric value of 2*k k z), when k is an even number, the value of the function with the same name is obtained, that is, the function name does not change;

When k is an odd number, the corresponding cofunction value is obtained, i.e., sin cos; cos→sin;tan→cot,cot→tan.(Odd and even unchanged).

It is then preceded by a sign that treats as the value of the original function when it is considered an acute angle. (See quadrant for symbols).

The above memorization mantra is:

Odd and even unchanged, and the symbol looks at the quadrant.

The symbol on the right side of the equation is the angle k·360° + k z), -180° 360°-, when considered as an acute angle

The sign of the original trigonometric value of the quadrant can be remembered.

The name of the horizontal induction remains unchanged; (See quadrant for symbols).

How to judge the symbols of various trigonometric functions in the four quadrants, you can also remember the formula.

A complete integrity; 2. Sine (cosecant); three and two cuts; Quadruple cosine (secant)".

Use odd and even invariant symbols to look at the quadrant and remember the recall.

e.g. sin(2+x).

2 is 1 times 2, is an odd number of mountain guesses, and the function name becomes cosine.

x is regarded as a sharp comic focal-shaped angle, then 2+x is in the second quadrant, and the second quadrant is sine positive, so sin( 2+x)=cosx

sin30°=1/2；sin30=cos30=；cos30°=√3/2

tan30=；tan30°=√3/3

sin45=；sin45°=√2/2

cos45=；cos45°=sin45°=√2/2tan45=；tan45°=1

sin60=；sin60°=√3/2

cos60=；cos60°=1/2

tan60=；tan60°=√3

sin90=；sin90°=cos0°=1cos90=；cos90°=sin0°=0tan90=；tan90° does not exist.

Application of the Induction Formula: Imitation Code.

General steps for transforming trigonometric functions using the induction formula:

Memorize the trigonometric values of special angles.

Pay attention to the inflection formula of the flexible use, and I am sure to sell it.

The requirements for trigonometric simplification are that the number of terms should be the least, the number of times should be the lowest, the name of the comma function should be the least, the denominator should be the simplest, and the value should be easily evaluated.

Remember the mantra, odd and even unchanged, and the symbol looks at the quadrant.

The meaning of "odd and even unchanged" is: for example, cos(270°- = - sin, 270° is 3 (odd) times of 90°, so cos becomes sin, that is, odd change; and sin(180°+ = - sin, 180° is 2 (even) times of 90°, so sin is still sin, i.e. even does not change.

"Symbol looking at quadrant" means that the quadrant that falls by the angle on the left side of the formula determines whether the right side of the formula is positive or negative. For example, cos(270°- = - sin, is regarded as an acute angle, 270°- is the third quadrant angle, and the cosine of the third quadrant angle is negative, so the right side of the equation is a negative sign.

For example, sin(180°+ = - sin, is regarded as an acute angle, 180°+ is the third quadrant angle, and the sine of the third quadrant angle is negative, so there is a negative sign on the right side of the equation. Note: In the formula, it can not be an acute angle, just to remember the formula, it is considered an acute angle.