Knowledgepoint of trigonometric function finding angle in mathematics (1)
Knowledgepoints of trigonometric function in mathematics (2)
Definition of inverse trigonometric function:
(1) arcsine: in the closed interval.
Meet the condition sinx=a(- 1? Answer? The angle x of 1) is called the arcsine of the real number A, and is denoted as arcsina, that is, x=arcsina, where x?
, and a = sinx
Note that the arcsine represents an angle with a sine value of A and an angle of in.
Within (-1? Answer? 1)。
(2) anti-cosine: in the closed interval
, in line with the conditions cosx=a(- 1? Answer? The angle x of 1) is called the anti-cosine of the real number a, and is denoted as arccosa, that is, x=arccosa, where x? [0,? ], and a=cosx.
(3) arc tangent: in the open interval
Within, the angle x that satisfies the condition tanx=a(a is a real number) is called the arctangent of real number a, and is denoted as arctana, that is, x=arctana, where x?
a=tanx。
Properties of inverse trigonometric functions;
( 1)sin(arcsina)= a(- 1？ Answer? 1)，cos(arccosa)=a(- 1？ Answer? 1),
tan(arctana)= a；
(2)arcsin(-a)=-arcsina，arccos(-a)=？ -arccosa，arctan(-a)=-arctana；
(3)arcsina+arccosa=
;
(4)arcsin(sinx)=x, only if X is
Internal establishment; Similarly, arccos(cosx)=x, only if x is in the closed interval [0,? ] established.
Steps to find the angle with known trigonometric function values:
(1) Determine the quadrant where the terminal edge of the angle is located (or the coordinate axis where the terminal edge is located) by the sign of the known trigonometric function value;
(2) If the function value is positive, first find the corresponding acute angle? 1, if the function value is negative, first find the acute angle corresponding to its absolute value? 1;
(3) According to the quadrant of the angle, 0~2 is obtained by the inductive formula. If the angle suitable for the condition is in the second quadrant, what is it? -? 1; If the right angle is in the third quadrant, what is it? +? 1; In the fourth quadrant, so it's 2? -? 1; What if it is -2? In the fourth frame, the angle to 0 is -0. 1, in the third quadrant is-? +? 1, in the second quadrant is-? -? 1;
(4) If all angles suitable for the conditions are required, the expressions with the angles of the same terminal edge are used to write.