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C12SineCosineRadians (1) презентация
Содержание
- 1. C12SineCosineRadians (1)
- 2. Sine rule
- 3. Exercise Calculate the value of and : a) b)
- 4. Town is 6 km, on a bearing
- 5. Let us find :
- 6. Exercise Work out the value of a) b)
- 7. Exercise Work out the value of and a) b)
- 8. When the angle to be found is
- 9. Exercise Work out the possible values of and the corresponding values of .
- 10. Cosine rule
- 11. Work out the value of the third side: Exercise
- 12. Exercise From a point a boat
- 13. Exercise Work out the size of
- 14. Exercise A helicopter flies on a
- 16. Area
- 17. Exercise Work out the area of the given triangle:
- 18. Exercise Work out the value of :
- 19. Angle is equal to 1 radian, when
- 20. radians , so radian
- 21. The length of an arc when is in radians.
- 22. The sector of the circle radius cm
- 23. Referring to the diagram, find: The
- 24. In the diagram is the diameter of
- 25. The area of a sector where is in radians
- 26. Exercise (a) (b) (c) Work out the area of the shaded region:
- 27. Exercise The arc of a circle,
- 28. The diagram shows a triangular plot of
- 29. In the diagram, is the diameter of
- 30. Exercise (C2 Jan 2010)
Sine rule
Слайд 1С12 Sine, cosine rules Radians
#sinerule #cosinerule #bearing #radian #arclength #sectorarea #trianglearea
Слайд 4Town is 6 km, on a bearing of 020, from town
. Town is located on a bearing of 055 from town and on a bearing of 120 from town .
Work out the distance of town from
a) town
b) town
Work out the distance of town from
a) town
b) town
Exercise
Слайд 8When the angle to be found is larger than the given
angle there are two possible results, because you can draw two different triangles which satisfy the task
These results and are connected:
These results and are connected:
In this example:
(to 3 s.f.)
Слайд 12Exercise
From a point a boat sails due north for 7
km to . The boat leaves and moves on a bearing of 100 for 10 km until it reaches .
Calculate the distance of from .
Calculate the distance of from .
Слайд 14Exercise
A helicopter flies on a bearing of 080 from to
, where km. It then flies for 60 km to a point .
Given that is 80 km from calculate the bearing of from .
Given that is 80 km from calculate the bearing of from .
Слайд 22The sector of the circle radius cm contains an angle of
radians. Find the length of the arc, giving your answers in the form , where and are integers.
Exercise
Слайд 23Referring to the diagram, find:
The perimeter of the shaded region when
radians.
The value of when the perimeter of the shaded region is 14 cm.
The value of when the perimeter of the shaded region is 14 cm.
Exercise
Слайд 24In the diagram is the diameter of a circle, centre and
radius 2 cm. The point lies on the circumference such that radians.
State the value, in radians, of .
The shaded region is a template for a brooch.
(b) Find the exact value of the perimeter of the brooch.
Exercise
Слайд 27Exercise
The arc of a circle, centre and radius cm, is
such that radians.
Given that the perimeter of the minor sector is 30 cm:
(a) Calculate the value of .
(b) Show that the area of the minor sector is 36 .
(c) Calculate the area of the segment enclosed by the chord and the minor arc .
Given that the perimeter of the minor sector is 30 cm:
(a) Calculate the value of .
(b) Show that the area of the minor sector is 36 .
(c) Calculate the area of the segment enclosed by the chord and the minor arc .
Слайд 28The diagram shows a triangular plot of land. The sides ,
and have lengths 12, 14 and 10 m respectively.
The lawn is a sector of a circle, centre and radius 6 m.
(a) Show that to 3 s.f.
(b) Calculate the area of the flowerbed.
Exercise
Слайд 29In the diagram, is the diameter of a circle, centre and
radius cm, and radians.
Given that the area of is equal to that of the shaded segment, show that
Exercise
