What type of triangle can the sine rule be used on?

The sine rule can be applied to any type of triangle . Unlike SOHCAHTOA, it is not restricted to right-angled triangles.

True or False? When using the inverse sine function , the result is always an acute angle.

True. When using the inverse sine function , the result is always an acute angle.

How can you find the corresponding obtuse angle when using the inverse sine function?

As the inverse sine function will always give you the acute angle, you must subtract this from 180º if you want to find the corresponding obtuse angle.

True or False? The cosine rule can only be applied to right-angled triangles.

False. The cosine rule can be used on any type of triangle . If, however, you have a right-angled triangle, it is often quicker to use SOHCAHTOA.

True or False? You should always check your calculator settings before completing any calculations involving trigonometry .

True. You must check that your calculator is in degrees mode and not radians or gradians mode to ensure that it will give you a correct answer. This is especially important to check before an exam !

True or False? When using the area of a triangle formula, the angle in question must be between the two sides .

True. When using the area of a triangle formula, the angle in question must be between the two sides .

Which trigonometric rule should be used if you know three sides of a triangle and want to work out a missing angle ?

If you know three sides of a triangle and want to work out a missing angle then the cosine rule should be used.

True or False? The cosine rule will sometimes give you an ambiguous answer for an angle.

False. The cosine rule will always give the correct answer for an angle, as long as the correct values are entered into the formula.

Which trigonometric rule should be used if you know the area of a triangle and two of its sides and you want to find the angle between those two sides ?

If you know the area of a triangle and two of its sides and you want to find the angle between those two sides , then the area of a triangle formula should be used.

True or False? Using the sine rule to find an angle may not result in the required angle .

True. Using the sine rule to find an angle will always generate the acute angle. If you need to find the obtuse angle, you will need to subtract the result from 180º .

Which trigonometric rule should be used if you know two sides of a triangle and the angle between them and you want to find the length of the third side ?

If you know two sides of a triangle and the angle between them and you want to find the length of the third side , then the cosine rule should be used.

True or False? In some exam questions you will be expected to use a combination of trigonometric rules or the same rule more than once .

True. In some exam questions you will be expected to use a combination of trigonometric rules or the same rule more than once .

True or False? The cosine rule should be used if you know two sides and the angle opposite one of the sides and you want to find the angle opposite the other side .

False. If you know two sides and the angle opposite one of the sides and you want to find the angle opposite the other side , then you should use the sine rule .

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IGCSEMathsCambridge (CIE)ExtendedFlashcardsPythagoras & TrigonometrySine, Cosine Rule & Area of Triangles

Sine, Cosine Rule & Area of Triangles (Cambridge (CIE) IGCSE Maths)

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FrontThe Sine Rule
State the equation for the sine rule.
BackThe Sine Rule
The equation for the sine rule is $\frac{a}{\sin (A)} = \frac{b}{\sin (B)} = \frac{c}{\sin (C)}$
Where:
$a$ is the length of the side opposite angle $A$
$b$ is the length of the side opposite angle $B$
$c$ is the length of the side opposite angle $C$
It can also be used in the form $\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}$

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State the equation for the sine rule.
The equation for the sine rule is $\frac{a}{\sin (A)} = \frac{b}{\sin (B)} = \frac{c}{\sin (C)}$
Where:
- $a$ is the length of the side opposite angle $A$
- $b$ is the length of the side opposite angle $B$
- $c$ is the length of the side opposite angle $C$
It can also be used in the form $\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}$
What type of triangle can the sine rule be used on?
The sine rule can be applied to any type of triangle.
Unlike SOHCAHTOA, it is not restricted to right-angled triangles.
True or False?
The sine rule can be used to find missing side lengths in non right-angled triangles.
True.
The sine rule can be used to find missing side lengths in non-right angled triangles.
It is easiest to do this when the equation is in the form with the angles in the numerators, $\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}$ .
How should the angles and sides of a triangle be labelled in order to apply the sine rule?
Angles should be labelled in capitals, $A$ , $B$ and $C$ .
Sides opposite to the angles should be labelled with the corresponding lower case letters, $a$ , $b$ and $c$ .
True or False?
When using the inverse sine function, the result is always an acute angle.
True.
When using the inverse sine function, the result is always an acute angle.
How can you find the corresponding obtuse angle when using the inverse sine function?
As the inverse sine function will always give you the acute angle, you must subtract this from 180º if you want to find the corresponding obtuse angle.
State the equation for the cosine rule in the form used to find a missing angle.
The equation for the cosine rule in the form used to find a missing angle is $\cos (A) = \frac{b^{2} + c^{2} - a^{2}}{2 b c}$
Where:
- $a$ is the length of the side opposite angle $A$
- $b$ and $c$ are the lengths of the two other sides
State the equation for the cosine rule in the form used to find a missing side.
The equation for the cosine rule in the form used to find a missing side is $a^{2} = b^{2} + c^{2} - 2 b c \cos (A)$
Where:
- $a$ is the length of the side opposite angle $A$
- $b$ and $c$ are the lengths of the two other sides
True or False?
The cosine rule can only be applied to right-angled triangles.
False.
The cosine rule can be used on any type of triangle.
If, however, you have a right-angled triangle, it is often quicker to use SOHCAHTOA.
True or False?
You should always check your calculator settings before completing any calculations involving trigonometry.
True.
You must check that your calculator is in degrees mode and not radians or gradians mode to ensure that it will give you a correct answer.
This is especially important to check before an exam!
What is the formula for the area of a triangle?
The area of a triangle is given by the formula $A = \frac{1}{2} a b \sin (C)$
Where:
- $A$ is the area of the triangle
- $a$ and $b$ are the lengths of two sides
- $C$ is the angle between those two sides
If $C = 90 °$ , what does the area formula for a triangle simplify to?
If $C = 90 °$ , the area formula for a triangle simplifies to $A = \frac{1}{2} b h$
Where:
- $A$ is the area of the triangle
- $b$ is the length of the base
- $h$ is the perpendicular height of the triangle
(This is because $\sin (90 °) = 1$ .)
How should the angles and sides of a triangle be labelled in order to apply the area of a triangle formula?
Angles should be labelled in capitals, $A$ , $B$ and $C$ .
Sides opposite to the angles should be labelled with the corresponding lower case letters, $a$ , $b$ and $c$ .
True or False?
When using the area of a triangle formula, the angle in question must be between the two sides.
True.
When using the area of a triangle formula, the angle in question must be between the two sides.
Which trigonometric rule should be used if you know three sides of a triangle and want to work out a missing angle?
If you know three sides of a triangle and want to work out a missing angle then the cosine rule should be used.
True or False?
The cosine rule will sometimes give you an ambiguous answer for an angle.
False.
The cosine rule will always give the correct answer for an angle, as long as the correct values are entered into the formula.
Which trigonometric rule should be used if you know the area of a triangle and two of its sides and you want to find the angle between those two sides?
If you know the area of a triangle and two of its sides and you want to find the angle between those two sides, then the area of a triangle formula should be used.
True or False?
Using the sine rule to find an angle may not result in the required angle.
True.
Using the sine rule to find an angle will always generate the acute angle.
If you need to find the obtuse angle, you will need to subtract the result from 180º.
Which trigonometric rule should be used if you know two sides of a triangle and the angle between them and you want to find the length of the third side?
If you know two sides of a triangle and the angle between them and you want to find the length of the third side, then the cosine rule should be used.
True or False?
In some exam questions you will be expected to use a combination of trigonometric rules or the same rule more than once.
True.
In some exam questions you will be expected to use a combination of trigonometric rules or the same rule more than once.
True or False?
The cosine rule should be used if you know two sides and the angle opposite one of the sides and you want to find the angle opposite the other side.
False.
If you know two sides and the angle opposite one of the sides and you want to find the angle opposite the other side, then you should use the sine rule.

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1. Topic 1
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2. Topic 2
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Sine, Cosine Rule & Area of Triangles (Cambridge (CIE) IGCSE Maths)

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