"Acute Angle Trigonometric Functions" PPT Courseware 5

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"Acute Angle Trigonometric Functions" PPT Courseware 5

1. As shown in the figure, in Rt△ABC, ∠C=90°, we call the ratio of the opposite side of the acute angle A to _________ the ________ of ∠A, and write it as sin A, that is, sin A=the opposite side of ∠A ( ) = ac, the ratio of the adjacent side of acute angle A to ________ is called ______ of ∠A, recorded as cos A, that is, cos A = adjacent side of ∠A () = bc.

2. The ________, ________ and ________ of acute angle A are all called ________ of ∠A.

3. sin 30°=_______, sin 45°=________,

sin 60°=________, cos 30°=________,

cos 45°=________, cos 60°=________．

【Error-prone Inventory】

[Example] Calculation: sin 30°+sin 245°-1/3tan 260°.

[Wrong solution] Original formula=1/2+(√2/2)2-1/3×(√3/3)2=1/2+1/2-1/9=8/9.

[Error Cause Analysis] Because the wrong trigonometric function values ​​lead to calculation errors, it is necessary to keep in mind the function values ​​of special angles.

【Integrated use】

twenty one. (12 points) In the right triangle in the figure, we know that sin α=ac, cos α=bc, tan α=ab, ∴sin 2α

+cos 2α＝a2c2＋b2c2＝a2＋b2c2＝c2c2＝1.

That is, the sum of the squares of the sine and cosine of an angle is 1.

(1) Please explore the relationship between sin α, cos α and tan α based on the above exploration process;

(2) Please use the conclusions of the above exploration to answer the following questions: It is known that α is an acute angle, and tan α=12. Find the value of sin α-2cos α2sin α+cos α.

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For more information about the "Acute Angle Trigonometric Functions" PPT courseware, please click on the Acute Angle Trigonometric Functions ppt tab.

"Applications of Acute Angle Trigonometric Functions" PPT courseware:

"Applications of Acute Trigonometric Functions" PPT courseware review and thinking about the relationship between the sides and angles of a right triangle. The relationship between the three sides of a right triangle: Pythagorean theorem a2+b2=c2. The relationship between the two acute angles of a right triangle: the two acute angles are mutually supplementary A+ B=900. Between the sides and angles of a right triangle...

"Calculation of Acute Angle Trigonometric Functions" PPT courseware:

"Calculation of Acute Angle Trigonometric Functions" PPT courseware 1. To use a calculator to find the value of an acute angle trigonometric function, you generally need to press the trigonometric function name key first, then enter the degree, use the degrees minutes and seconds keys to distinguish the degree unit, and finally press the = key. For example: use a calculator to find the value of cos 10. Press the keys in sequence. .

"Acute Angle Trigonometric Functions" PPT Courseware 4:

"Trigonometric Functions of Acute Angles" PPT Courseware 4 1. As shown in the figure, in Rt△ABC, C=90, we call the ratio of the opposite side of A to ________ as the tangent of A, and record it as tan A, that is, tan A=opposite side of A/adjacent side of A= ab. 2. tan 30=________, tan 45=_____..

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Update Time: 2024-10-03

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

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