Teaching plan of inductive formula of tangent function in senior two mathematics.

learning target

1, further understand the idea of combining numbers and shapes, and improve the ability of analyzing and solving problems;

2. The inductive formula of tangent function can be deduced from the inductive formula of sine and cosine function;

3. Master the application of inductive formula in evaluation and simplification.

Inductive formula of tangent function of learning focus and its application

Derivation of inductive formula of tangent function of learning difficulties

learning process

First, preview self-study

1. Look at the number 1-46 on page 38 of the textbook. When-4 14 < 4 14 < 414, what is the relationship between angle 414 and tangent function value of angle 2?

We can get the following formula:

tan(2 4 14)= tan(-4 14)= tan(2 4 14)= tan

Tan (4 14 = Tan (4 14 =

2. We can use the inductive formula to transform the trigonometric function problem of any angle into the trigonometric function problem of acute angle. Refer to the block diagram below and think about which formulas should be used for each transformation.

4 14

Fill in the corresponding words on the arrow above.

Second, cooperative exploration.

Explore 1, and try to derive the formula tan (4 14, Tan 4 14) by using the induction formula of sine and cosine function of 414.

Inquiry 2 If tan 4 14, define sine function value and cosine function value of angle finding 4 14 with trigonometric function.

Explore 3 to find the value of 4 14.

Third, standard testing

1 The following statement is true ()

A tan (4 14 =- tan 4 14 B tan (4 14 = tan 4 14)

c tan(-4 14)=-tan 4 14D tan(2 4 14)= tan 4 14

2 Find the following trigonometric function values

(1) Tan (-4 14 (2) Tan 240 4 14 4 14 (3) Tan (-1574 4 14)