"Trigonometric Ratio of Acute Angles" PPT courseware

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"Trigonometric Ratio of Acute Angles" PPT courseware

How to find the angle of the tower centerline from the vertical centerline

This question involves the knowledge of acute angle trigonometric functions. After studying this chapter, you can easily answer this question!

think

In the above question, if the height of the water outlet is 50m, how long of the water pipe needs to be prepared?

Conclusion: In a right triangle, if an acute angle is equal to 30°, then regardless of the size of the triangle, the ratio of the opposite side of the angle to the hypotenuse is equal to 1/2

As shown in the figure, draw an arbitrary Rt△ABC so that ∠C=90° and ∠A=45°. Calculate the ratio BC/AB of the opposite side of ∠A to the hypotenuse. What conclusion can you draw?

That is, in a right triangle, when an acute angle is equal to 45°, regardless of the size of the right triangle, the ratio of the opposite side of the angle to the hypotenuse is equal to √2/2

Example question demonstration

Example 1 As shown in the figure, in Rt△ABC, ∠C=90°, find the values ​​of sinA and sinB.

Solution: In Rt△ABC, because AC=4, BC=3, so AB=5,

∴SinA=BC/AB=3/5

SinB=AC/AB=4/5

To find sinA is to determine the ratio of the opposite side of ∠A to the hypotenuse; to find sinB is to determine the ratio of the opposite side to ∠B and the hypotenuse.

Example 2. As shown in the figure, in Rt △ABC, ∠C=90°, AB=13, BC=5

Find the values ​​of sinA and sinB.

Solution: In Rt △ABC,

sinA=BC/AB=5/13

AC=√AB²-BC²=√13²-5²=12

∴sinB=AC/AB=12/13

think about it

1. As shown in the figure, ∠C=90°CD⊥AB.

sinB can be determined by the ratio of which two line segments?

If AC=5, CD=3, find the value of sinB.

Solution: ∵∠B=∠ACD

∴sinB=sin∠ACD

In Rt△ACD, AD=√AC²-CD²=√5²-3²=4

sin∠ACD=AD/AC=4/5

∴sinB=4/5

To find the sine of an angle, in addition to directly using the definition, it can also be converted into the sum of the sine of its equal angles.

Application examples

1. In Rt △ABC, ∠C=90°, find the trigonometric function value of ∠A.

① a=9 b=12 ② a=9 b=12

2. In △ABC, AB=AC=4, BC=6, find the trigonometric function value of ∠B.

3. It is known that ∠A is an acute angle, sinA=15/17, find the values ​​of cosA and tanA.

4. As shown in the figure, in Rt△ABC, ∠C=90°, AC=8, tanA=3/4, find the values ​​of sinA and cosB.

Review Summary

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, and tanA are ratios (numeric values).

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

Keywords: Acute angle trigonometric ratio teaching courseware, Qingdao edition ninth grade mathematics volume PPT courseware download, ninth grade mathematics slide courseware download, acute angle trigonometric ratio PPT courseware download, .PPT format;

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Update Time: 2024-07-01

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

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