Junior high school mathematics trigonometric function memory formula trigonometric function is a function, and quadrant symbols are marked.
Function image unit circle, periodic parity increase and decrease.
The same angle relation is very important, and both simplification and proof are needed.
At the vertex of the regular hexagon, cut the chord from top to bottom;
Write the number 1 in the middle to connect the vertex triangles.
The sum of the squares of the downward triangle, the reciprocal relationship is diagonal,
Any function of a vertex is equal to the division of the last two.
The inductive formula is good, negative is positive and then big and small,
It is easy to look up the table by turning it into an acute angle, and it is essential to simplify the proof.
Half of the integer multiple of π, with the odd even unchanged,
The latter is regarded as an acute angle, and the sign is judged as the original function.
The cosine of the sum of two angles is converted into a single angle, which is convenient for evaluation.
The calculation proves that the angle is the first, pay attention to the name of the structure function,
Keep the basic quantity unchanged, from difficult to simple.
Guided by the principle of reverse order, the product of rising power and falling power and difference.
The proof of conditional equality, the idea of equation points out the direction.
Universal formula is unusual, rational formula is ahead.
The formula is used in the right and wrong direction, and the deformation is used skillfully;
Add cosine as cosine, subtract cosine as sine,
The power-on angle is halved, and the power-on angle is reduced by one norm;
The essence of the inverse function of trigonometric function is to find the angle.
First find the trigonometric function value, and then determine the angle range;
Using right triangle, the image is intuitive and easy to rename.
The equation of a simple triangle is reduced to the simplest solution set.
Trigonometric function induces formula memory. The names of formula 1 to formula 5 have not changed, but the name of formula 6 has changed.
Formulas 1 to 5 can be abbreviated as: the name of the function is unchanged, and the symbol depends on the quadrant. That is, the trigonometric function values of α+k 360 (k ∈ z), ﹣ α, 180 α, and 360-α are equal to the trigonometric function values of the same name, preceded by a sign of the original function value when α is regarded as an acute angle.
The above inductive formula can be summarized as follows:
For the trigonometric function value of kπ/2 α (k ∈ z),
① When k is an even number, the function value of α with the same name is obtained, that is, the function name is unchanged;
② When k is an odd number, the cofunction value corresponding to α is obtained, that is, sin→cos；; cos→sin； Brown → canvas bed, canvas bed → brown (even odd number, even constant), and then when α is regarded as an acute angle, add the sign of the original function value. (Symbols look at quadrants)
Formula: Odd numbers change to even numbers, and symbols look at quadrants.
Note: Parity is unchanged (for k, it means that k is odd or even), and the sign is in the quadrant (see the original function, α can be regarded as an acute angle).
The symbols on the right side of the formula are: when α is regarded as an acute angle, the symbols of the original trigonometric function values in the quadrants of angles k 360+α (k ∈ z),-α, 180 α and 360-α can be memorized: the horizontal induced name is unchanged; Symbols look at quadrants.
How to judge the symbols of various trigonometric functions in four quadrants, you can also remember the formula "a full pair; Two sine (cotangent); Cut in twos and threes; Four cosines (secant) ".
The meaning of this 12 formula is:
The trigonometric function value of any angle in the first quadrant is "+";
In the second quadrant, only sine and cotangent are "+",and the rest are "-";
In the third quadrant, only the tangent and cotangent are "+",and other functions are "-";
In the fourth quadrant, only secant and cosine are "+",and the rest are "-".
One full sine, two sines, three double tangents and four cosines.