How do you remember trigonometric formulas? Induction formula

Memorize more, memorize more, and write more on paper.

Memorize it down, then.

Do the same kind of questions, and you will.

Master the use of formulas.

Sine: 1 plus the tangent square to divide the tangent times, pay attention to the meaning of 'divide'.

Cosine: Yin and Yang are cosines compared to cosine.

Trigonometric memory slips through the mouth Methods and techniques of memorization.

The commonly used induction formulas for trigonometric functions are: sin(2k +a)=sina (k z), cos(2k +a)=cosa (k z), tan(2k +a)=tana (k z), cot(2k +a) = cota (k z), etc.

The relationship between the trigonometric value of and the trigonometric value of . Bulk selling.

Let be an arbitrary angle, a representation of the angle under the radian system:

sin（π+sinα.

cos（π+cosα.

tan（π+tanα.

cot（π+cotα.

sec（π+secα.

csc（π+cscα.

Representation of angles under the angle system:

sin（180°+αsinα.

cos（180°+αcosα.

tan（180°+αtanα.

cot（180°+αcotα.

sec（180°+αsecα.

csc（180°+αcscα.

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

sin（-αsinα.

cos（-αcosα.

tan（-αtanα.

cot（-αcotα.

sec（-αsecα.

csc (-cscα.

Using Equations 2 and 3, we can get the relationship between - and the trigonometric value of

Representation of angles in radians:

sin（π-sinα.

cos（π-cosα.

tan（π-tanα.

cot（π-cotα.

sec（π-secα.

csc（π-cscα.

Representation of the angle system under the angle system:

sin（180°-αsinα.

cos（180°-αcosα.

tan（180°-αtanα.

cot（180°-αcotα.

sec（180°-αsecα.

csc（180°-αcscα.

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)".

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.

1: Remember that the four basic functions have positive and negative values in each quadrant, the sine quadrant is positive, the cosine quadrant is positive, the tangent and cotangent quadrants are positive, and the others are negative.

2: Remember the transformation period, the sine and cosine are 2, and reduce the angle to the simplest angle (that is, divide by the transformation period), for example, sin(13 2 ) = sin(6 + 2 ) = sin( 2 ) When the added angle appears 2 or 3 2, the sine and cosine call, and the sine and cotangent are interchanged, in this case, it must be a cosine.

3. Name all the angles as the first quadrant angle, and then rotate the angle to be angled, and the number of quadrants that fall on it is equal to the added quadrant symbol of this angle. For example, sin(2) is the angle of the first quadrant, and - is the angle of the fourth quadrant, then - + 2 falls in the first quadrant, so sin(2)=cos can be obtained from 2.

Example: cot(19 2+) = cot(3 2+8 + = cot(3 2+) = tan

Hello! (Odd and even unchanged).

For example, if k is an odd number in sin(k 2+) (e.g. 2......）

sin becomes cos, and even numbers do not change (e.g., ...).

In the same way, if k in cos(k 2+) is an odd number (e.g. 2......）

cos becomes sin, and even numbers do not change (e.g., ...).

Similarly, there are tan to cot and cot to tan

(See quadrant for symbols).

Example: sin(2+)=cos

When you think of as an acute angle (first quadrant), 2+ is the second quadrant angle and sin( 2+ ) is a positive number.

Therefore the cos sign is positive.

cos(π/2+α)=-sinα

When you think of is an acute angle (first quadrant), 2+ is the second quadrant angle, and cos(2+) is negative.

Hence the sin sign is negative.

sin(π/2-α)=cosα

When considering as an acute angle (first quadrant), 2- is still the first quadrant angle, and sin(2- ) is a positive number.

Therefore the cos sign is positive.

cos(π/2-α)=sinα

When considering as an acute angle (first quadrant), 2- is still the first quadrant angle, and cos(2- ) is a positive number.

Therefore the cos sign is positive.

It's all my own experience.

It's finally over. I'm tired. The landlord adds a few points!

Induction formulaIn a word: the odd and the even do not change, and the symbol looks at the quadrant.

Think of any angle as k·(2).

or k·(2)-

If k is an odd number, the function name changes accordingly: sin cos, cos sin, tan cot, cot tan

The angle will become (if you don't know the size of , all default is an acute angle, which does not affect the final result) The symbol looks at the quadrant refers to the trigonometric symbol corresponding to the quadrant where the original angle is located, just add the symbol in front of it.

For example: sin(.]

sin[2·（π/2）＋α=

SIN explains:

is twice as much as 2, so the function name remains the same, and it is still sin

is the third quadrant angle, and the corresponding sin sign is a negative sign, so a negative sign "—" is added in front of the result

The result is: sinα

Also note: k·(2).

or k·( 2)- after the change, the angle is , regardless of the + and - in front of it.