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What are the arc length formula and sector area formula
Arc length formula: n is the degree of circle center angle, R is the radius, α Is the arc of the center angle of the circle. L = n π R ÷ 180 or L = n / 180 · π R or L=| α| R in a circle with radius r, because the arc length of the center angle of 360 ° is equal to the circumference length C = 2 π R, the arc length of the center angle of n ° is L = n π R ÷ 180
Trigonometric function representation of triangular area formula
Because: S = 1 / 2ah, H = bsinc; Then: S = 1 / 2 absinc
Similarly: S = 1 / 2ah ', H' = csinb, then: S = 1 / 2 acsinb;
Or: S = 1 / 2bh '', H '' = csina, then: S = 1 / 2 bcsina
The formula of triangular area is expressed by trigonometric function
In triangle ABC, s = 0.5 × bcsinA=0.5acsinB=0.5absinC
Calculation formula of trigonometric function (the simplest) Pay attention to the basic formula of junior middle school!
The calculation formulas of trigonometric function that junior middle school students should master include:
1. Define formula
In right triangle ABC, angle c is a right angle
sinA=cosB=a/c,sinB=cosA=b/c,tanA=cotB=a/b
2. Simple relation formula
sin^2A+cos^2A=1,tanAcotA=1
Other formulas will not be learned and used until high school
It is known that the arc length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of the center angle of the arc is __
As shown in the figure,
△ ABC is an inscribed regular triangle of ⊙ o with radius r,
Then BC = 2CD = 2rsin π
3=
3r，
Let the number of radians of the center angle of the arc be α，
Then R α=
3r，
Solution α＝
3．
So the answer is:
3．
If the circumference of a sector with a radius of 1 is equal to the arc length of the semicircle of its circle, what arc is the center angle of the sector? What is the area of the fan?
Radius r = 1, arc length L of sector, sector perimeter = L + R + r = L + 2;
Arc length of semicircle = 2 π * 1 / 2 = π;
L+2=π,L=π-2;
The radius is 1, so the center angle of the sector = π - 2 (radians), [or, the center angle of the sector: 2 π = (π - 2): 2 π * 1]
Area of sector = L * r / 2 = (π - 2) * 1 / 2 = π / 2-1
RELATED INFORMATIONS
- 1. If the circumference of a sector with a radius of 2 is equal to the arc length of the semicircle, then the center angle of the sector is___ Radian, sector area is _
- 2. It is known that the arc length of an arc is equal to the side length of the inscribed regular triangle of its circle, then the radian number of the center angle of the arc is __
- 3. In a circle, the length of an arc is 6 / 15 of the circumference of the circle. Find the degree of the center angle of the circle opposite the arc Triangle ABC is an equilateral triangle with a side length of 50cm. Draw an arc with points a, B and C as the center and 50cm as the radius, and find the sum of the three arc lengths (Note:
- 4. If a string divides a circle into two arcs of 1:3, the circumferential angle of the string is
- 5. If the radius of circle O is 2, the length of a chord is twice the root sign 3, and the center angle of the chord is
- 6. A chord with a length equal to the radius has a central angle equal to______ Radians
- 7. The arc length corresponding to the center angle of 60 ° is () of the circumference of the circle
- 8. If the length of a chord of a circle is equal to its radius, the degree of the circumferential angle of the chord is () A. 30 ° or 60 ° B. 60° C. 150° D. 30 ° or 150 °
- 9. It is known that triangle ABC and point m satisfy Ma + MB + MC = 0. If there is a real number m such that ab + AC = mam holds, then M is equal to
- 10. Known vector a = (1,2), B = (COS) α, sin α), Let m = a + TB (t is a real number) if α= π / 4, find the absolute value of M, and when the minimum value is taken, the value of T
- 11. Questions about the radian system of mathematics in Senior High School Why is 1 radian equal to 180 ° / π, and why is 1 ° equal to (π / 180) rad?
- 12. Please, I want to take the exam. It's a little difficult to find the formula now
- 13. Conversion of angle and radian What angle is a radian equal to
- 14. Prove the calculation formula of sector area with radian system s = 0.5rl
- 15. Conversion of radian system and angle system Let the radian number of an angle be a and the angle be n degrees, then a (RAD) =?
- 16. There is a road construction brigade to build an arc-shaped curve, whose radius R is 36cm, and the center angle of the arc is 60 degrees, then how many cm is the length of the curve, expressed in π
- 17. The chord length and radius are known. To calculate the arc length, the formula is required
- 18. If the arc length opposite the center angle of 2 radians is 4cm, the area of the sector sandwiched by the center angle is ___
- 19. How to calculate the radius of an arc with known chord length and arch height? Given the chord length and arch height, the formula for finding the radius? Given the arc length and arch height, the formula for calculating the chord length?
- 20. The formula for calculating the center angle of a circle with known arc length and radius of a sector