"Acute Angle Trigonometric Functions" PPT Courseware 2

Description

"Acute Angle Trigonometric Functions" PPT Courseware 2

learning target

1. Further consolidate the definition of trigonometric functions such as sine, cosine and tangent of an acute angle;

2. Master the values ​​of various trigonometric functions at angles of 30°, 45°, and 60°;

3. Learn to use a calculator to find the trigonometric function value of an angle;

4. Feel the connection between mathematics and the objective world, and experience the fun of cooperation, communication and exploration of mathematics.

Several issues that should be noted in the definition:

1. sinA, cosA, and tanA are defined in a right triangle, and ∠A is an acute angle (pay attention to the combination of numbers and shapes to construct a right triangle).

2. sinA, cosA, tanA is a ratio (numeric value).

3. The sizes of sinA, cosA, and tanA are only related to the size of ∠A, and have nothing to do with the side lengths of the triangle and the angle.

Warm-up before school

1. As shown in the figure, in △ABC, the two sides AB and AC of the acute angle A are expanded by 100 and 10 times respectively, and the value of tanA ( )

A. Expand 10 times B. Reduce 10 times

C. unchanged D. uncertain

2. In the figure below, ∠ACB=90°, CD⊥AB, and the vertical foot is D.

tanA =( )/AC=CD/( )=BD/CD

Example 1 Find the values ​​of the following expressions:

(1) cos260° + sin260°

(2) cos45°/sin45°-tan45°

(3)tan45°.sin45°-4sin30°.cos45°+cos230°

Consolidate training

1. Find the values ​​of the following expressions:

(1) 1-2 sin30°cos30°

(2) 3tan30°-tan45°+2sin60°

(3) cos60°/1+sin60°+1/tan30°

2. As shown in the figure, in Rt△ABC, ∠ACB=90°, CD⊥AB at D, knowing ∠B=30°, calculate the value of tan∠ACD+sin∠BCD.

3. In Rt△ABC, ∠C=90°, tanA+tanB=4, the area of ​​△ABC is 8, find the length of AB.

4. In Rt△ABC, ∠C=90°.

Verify: sin2A+cos2A=1.

Operation

1. Workbook: Textbook P82, Exercise 28.1 Question 3;

2. Quality monitoring: P43-45: 28.1(3)(4). Group A, Group B;

3. Study test 2+1, 10 minutes in class: P59-60.

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Update Time: 2024-11-06

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 2 industry PPT template

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