"Trigonometric Ratios of 30°, 45°, and 60° Angle" PPT Courseware 2

Description

"Trigonometric Ratios of 30°, 45°, and 60° Angle" PPT Courseware 2

learning target:

1. Experience the process of exploring the trigonometric ratios of angles 30°, 45°, and 60°, know how to find the values ​​of the trigonometric ratios of these special angles, and memorize the values ​​of the trigonometric ratios of these special angles.

2. Can directly find the corresponding acute angle based on the value of a trigonometric ratio of 30°, 45°, and 60° angles.

3. Be able to calculate the values ​​of formulas containing special angle trigonometric ratios.

Learning points:

1. Go through the process of exploring the trigonometric ratios of angles 30°, 45°, and 60°, and memorize the values ​​of these trigonometric ratios.

2. Use trigonometric ratios of 30°, 45°, and 60° angles to perform calculations

Learning difficulties:

Explore the trigonometric ratios of 30°, 45°, and 60° angles

Pre-class knowledge preparation:

1. The acute trigonometric ratio is defined by the ratio of the sides of a right triangle. How are the trigonometric ratios of acute angle α defined?

2. Observe what sharp angles there are in a set of triangles?

3. Simplify: 1/√2=______ 2/√3=________

Review the past and learn the new

1. Review and introduce new knowledge:

Review the definition of acute angle trigonometric ratios and find the following trigonometric ratios:

As shown in the figure: In Rt△ABC, ∠C=90° BC=1, AC=2,

Then sinA=____, cosA=____, tanB=______

2. Independent learning and cooperative inquiry

Experiment and exploration one

Using the properties of a triangle ruler with an angle of 45°, according to the definition of acute angle trigonometric ratio, can you explore the values ​​of sin45°, cos45°, and tan45° respectively?

Experiment and Exploration 2

Using the above method, can you continue to explore the values ​​of sin30°, cos30°, and tan30°?

Experiment and exploration three

Using the above conclusion, I believe you will be able to find the values ​​of sine, cosine and tangent of an angle of 60°. Let’s start now!

3. Analysis of classic examples and detailed explanations

Example 1. Find the values ​​of the following formulas:

(1) sin30°·cos45° (2) tan45°-cos60°.

Solution: (1) sin30°·cos45°=1/2×√2/2=√2/4

(2) tan45°-cos60°＝1-1/2=1/2

Example 2. In Rt△ABC, it is known that sinA=√3/2, find the degree of acute angle A.

Solution: Because A is an acute angle, and sinA =√3/2, and since sin60 °=√3/2, so ∠A= 60 °.

4. Cooperation and exchange, challenge yourself

As shown in the figure, construct a square ABCD with side length 1. Extend side CB to D′, make BD′=BD, and connect DD′.

Can you use this graph to find the value of the tangent of the angle 22.5°? Give it a try.

5. Training to meet standards and improve abilities

1. It is known that ∠A and ∠B are acute angles. If cosA=1/2, then ∠A= ,

If tanB=√3, then ∠B=_____

2. If tan(α-30°)=1, then ∠α= _____

3. As shown in the figure on the right, in the obtuse angle △ABC, ∠A=30°, then the value of sinA is ( )

A.√3/2 B. Does not exist C.1/2 D. Unable to determine

4. In △ABC, ∠A and ∠B are both acute angles, and sinA=1/2, cosB=√3/2, then △ABC is ( )

A. Right triangle B. Acute triangle C. Obtuse triangle D. Uncertain

Keywords: Trigonometric ratio teaching courseware for angles 30°45°60°, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, Trigonometric ratio of angles 30°45°60° PPT courseware download, .PPT Format;

For more information about the PPT courseware "Trigonometric Ratios of Angle 30°45°60°", please click on the Trigonometric Ratios of Angle 30°45°60° ppt tag.

"Trigonometric Ratios of Angle 30°45°60°" PPT courseware 3:

"Trigonometric Ratio of 304560 Angles" PPT Courseware 3 Review the past and learn the new 1. The sine of A: sinA = the opposite side of A/the hypotenuse The cosine of A: cosA =the adjacent side of A/the tangent of the hypotenuse A: tanA =the opposite side of A/the adjacent side of A The sine, cosine, and tangent of the acute angle A are collectively called The trigonometric ratio of acute angle A..

"Trigonometric Ratios of Angle 30°45°60°" PPT courseware:

"Trigonometric Ratio of 304560 Angle" PPT courseware learning objectives 1. Experience the process of exploring the trigonometric function value of 304560 angle, be able to make relevant reasoning, and further understand the significance of trigonometric functions. 2. Be able to calculate the trigonometric function value of 304560 angle. 3. Ability to act according to 3..

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Update Time: 2024-10-05

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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