"Values ​​of trigonometric functions for angles of 30°, 45°, and 60°" Relationship between sides and angles of a right triangle PPT courseware 4

Description

"Values ​​of trigonometric functions for angles of 30°, 45°, and 60°" Relationship between sides and angles of a right triangle PPT courseware 4

question

As shown in the figure, in Rt△ABC, ∠C=90°, AC=a, ∠A=30°, find BC.

analyze

1. From ∠C=90°, ∠A=30°, what do we think of?

2. Assuming BC=x, then what is AB equal to?

3. How to find BC next?

new lesson

Observe a set of triangles. How many acute angles are there? How many degrees do they equal?

⑴What is sin30°? How did you get it? Communicate with your peers.

⑵What is cos30° equal to? What about tan30°?

Do it

⑴What are the values ​​of the trigonometric functions for an angle of 60°? How did you get it?

⑵What are the values ​​of the trigonometric functions for an angle of 45°? How did you get it?

⑶ Complete the following table:

Think about it:

If you know the value of a certain trigonometric function for an acute angle, can you find the acute angle?

For example, tanA=1, what is the acute angle A?

Example analysis

Example 1 Calculation

⑴ sin30°＋cos45°;

⑵ sin260°＋cos260°－tan45°.

Example 2 A child is swinging on a swing. The length of the swing chain is 2.5m. When the swing swings to both sides, the swing angle is exactly 60°, and the swing angles on both sides are the same. Find the angle between when it swings to the highest position and when it swings to the lowest position. Difference in height (result is accurate to 0.01m).

Solution: As shown in the figure, according to the meaning of the question, we can know that

∠AOD＝ ×60°＝30°, OD＝2.5m,

∴OC＝ODcos30°＝2.5×√3/2≈2.165（m）

∴AC＝2.5－2.165 ≈0.34 (m)

Therefore, the height difference between the highest position and the lowest position is about 0.34m.

Practice in class

⒈Calculation:

⑴ sin60°-tan45°;

⑵ cos60°＋tan60°;

⑶√2/2sin45°+sin60°－2cos45°

⒉There is an escalator in a shopping mall with an inclination angle of 30° and a height of 7m. What is the length of the escalator?

Keywords: teaching courseware on the relationship between sides and angles of a right triangle, teaching courseware on trigonometric function values ​​of angles 30°, 45° and 60°, Beijing Normal University edition ninth grade mathematics volume 2 PPT courseware, ninth grade mathematics slide courseware download, sides of a right triangle Angle relationship PPT courseware download, trigonometric function values ​​of 30°45°60° angle PPT courseware download, .ppt format

For more information about the PPT courseware "The relationship between the sides and angles of a right triangle and the value of the trigonometric function of the angle 30°45°60°", please click the "The relationship between the sides and angles of a right triangle ppt The value of the trigonometric function of the angle 30°45°60°" ppt tag.

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"Trigonometric Function Values ​​of Angle 30, 45, and 60" PPT courseware on the relationship between the sides and angles of a right triangle. Learning objectives of this lesson: 1. Use the definition of trigonometric functions to find the trigonometric function values ​​of the special angles 30, 45, and 60. 2. Be able to perform 30, 45. Calculation of trigonometric function values ​​of 60 angles. 3. Can...

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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