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Authoritative PPT Summary
"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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