Special trigonometric function value comparison table
Sine and cosine values of formulas of trigonometric functions 30, 45 and 60 are in * * *: denominator is 2. If all molecules are added with the root sign, the number of roots will correspondingly become 1, 2, 3. The characteristic of tangent is to add all the molecules with root signs, so that the value of denominator is 3, and the corresponding number of roots will be 3.
Memory formula 1
Thirty, forty-five, sixty degrees, trigonometric function firmly remember;
The denominator chord bisector is three, and the numerator should add a root sign;
One, two, three, three, two, one, three, nine, twenty-seven;
The tangent function and sine function increase, and the cosine function decreases.
Memory formula 2
One, two, three, two, one, put the root sign and split it in half.
Count three on both sides, with a flagpole in the middle.
Distinguish between increase and decrease, and try to put the denominator.
It's easy to remember and simple.
Zero and ninety degrees, diagonal Z-shaped connection.
All endpoints are zero, and the rest are filled vertically and horizontally.
The symbolic memory formula for judging the value of trigonometric function is: odd variables are unchanged, and symbols look at quadrants.
For the trigonometric function value of π/2 * k 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； Tan → Kurt, Kurt → Tan. (even odd numbers remain unchanged), and then add the sign of the original function value when α is regarded as an acute angle. (Symbols look at quadrants)
Example:
Sin (2π-α) = sin (4 π/2-α), and k=4 is an even number, so we take sinα.
When α is an acute angle, 2 π-α ∈ (270,360), sin (2π-α)
So sin(2π-α)=-sinα.
The symbolic formula of trigonometric function in four quadrants is "one is positive; Two sine (cotangent); Cut in twos and threes; Four cosines (secant) ".
The four trigonometric functions at any angle in the first quadrant are "+";
In the second quadrant, only the sine is "+",and the rest are "-";
The tangent function of the third quadrant is+and the chord function is-.
In the fourth quadrant, only cosine is "+",others are "-".