True or False? Pythagoras' theorem can be applied to any type of triangle .

False. Pythagoras' theorem can not be applied to any type of triangle . It can only be applied to right-angled triangles.

True or False? The hypotenuse is always the longest side of a right-angled triangle .

True. The hypotenuse is always the longest side of a right-angled triangle .

True or False? SOHCAHTOA can be used in 3D problems.

True. SOHCAHTOA can be used in 3D problems.

What is a plane in geometry?

A plane in geometry is a flat , two-dimensional surface that extends infinitely in all directions.

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

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

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 the correct angle mode to ensure that it will give you a correct answer. It should be set to radians or degrees depending on the question. 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.

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.

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 .

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.

A bearing is a way of describing and using a direction as an angle .

From which compass direction should a bearing always be measured?

A bearing should always be measured from North .

True or False? Bearings are measured in an anti-clockwise direction.

False. Bearings are measured in a clockwise direction.

How many figures must a bearing be written with?

A bearing must be written with 3 figures . For angles under 100°, zero(es) should be used to fill in the missing figures, e.g. 059º, 008º.

True or False? SOHCAHTOA and Pythagoras' theorem are frequently used in bearings questions.

True. Pythagoras' theorem and SOHCAHTOA are frequently used in bearings questions. This is because situations often include finding missing lengths or angles in right-angled triangles .

If a bearing of A from B is known, how do you find the bearing of B from A ?

If a bearing of A from B is less than 180 o , then add 180 o to find the bearing of B from A. E.g. if the bearing of A from B is 030 o , then the bearing of B from A is 210 o . If a bearing of A from B is greater than 180 o , then subtract 180 o to find the bearing of B from A. E.g. if the bearing of A from B is 270 o , the bearing of B from A is 090 o .

Which compass direction is indicated by a bearing of 090° ?

When a bearing is 090°, it means due east .

True or False? North should always be indicated on a diagram.

True. North should always be indicated on a diagram as a point of reference.

Which trigonometric ratio is often used in problems involving angles of elevation and depression?

The trigonometric ratio that is often used in real-life scenarios with angles of elevation and depression is the tangent ratio . This is because real-life questions are often concerned with the height of an object (the 'opposite' side) and the horizontal distance from an object (the 'adjacent' side).

IBMathsDPApplications & Interpretation (AI)HLFlashcards3. Geometry & TrigonometryTrigonometry

Trigonometry (DP IB Applications & Interpretation (AI))

Flashcards

1/39

FrontPythagoras & Right-Angled Trigonometry
State the formula for Pythagoras' theorem.
BackPythagoras & Right-Angled Trigonometry
The formula for Pythagoras' theorem is $a^{2} + b^{2} = c^{2}$
Where:
$a$ and $b$ are the lengths of the two shorter sides
$c$ is the length of the hypotenuse
This formula is not given in the formula booklet.

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Cards in this collection (39)

State the formula for Pythagoras' theorem.
The formula for Pythagoras' theorem is $a^{2} + b^{2} = c^{2}$
Where:
- $a$ and $b$ are the lengths of the two shorter sides
- $c$ is the length of the hypotenuse
This formula is not given in the formula booklet.
True or False?
Pythagoras' theorem can be applied to any type of triangle.
False.
Pythagoras' theorem can not be applied to any type of triangle.
It can only be applied to right-angled triangles.
True or False?
The hypotenuse is always the longest side of a right-angled triangle.
True.
The hypotenuse is always the longest side of a right-angled triangle.
True or False?
When finding a non-hypotenuse side using Pythagoras' theorem, you add inside the square root.
E.g. for a triangle with hypotenuse of length 8 cm and another side of 3 cm, the remaining side, of length $x$ cm, can be found using the calculation $x = \sqrt{8^{2} + 3^{2}}$ .
False.
When finding a non-hypotenuse side, you subtract inside the square root.
E.g. for a triangle with hypotenuse of length 8 cm and another side of 3 cm, the remaining side, of length $x$ cm, can be found using the calculation $x = \sqrt{8^{2} - 3^{2}}$ .
State the 3D version of the Pythagoras' theorem formula.
The 3D version of Pythagoras' theorem is $d^{2} = x^{2} + y^{2} + z^{2}$
Where:
- $d$ is the straight line distance between two points
- $x$ is the distance in the $x$ -direction between the two points
- $y$ is the distance in the $y$ -direction between the two points
- $z$ is the distance in the $z$ -direction between the two points
This is not given in your exam formula booklet.
How are the sides in a right-angled triangle labelled for trigonometry?
The three sides are labelled the Hypotenuse (the side opposite the right-angle), the Adjacent (the side next to the angle in question) and the Opposite (the side opposite the angle in question).
What does SOHCAHTOA stand for?
SOHCAHTOA stands for:
- Sine is Opposite over Hypotenuse, $\sin θ = \frac{O}{H}$
- Cosine is Adjacent over Hypotenuse, $\cos θ = \frac{A}{H}$
- Tangent is Opposite over Adjacent, $\tan θ = \frac{O}{A}$
What does the inverse trigonometric function do, e.g. $\sin^{- 1}$ ?
The inverse trigonometric function is used to find missing angles when two sides of a right-angled triangle are known.
E.g. $θ = \sin^{- 1} (\frac{Opposite}{Hypotenuse})$ .
True or False?
SOHCAHTOA can be used in 3D problems.
True.
SOHCAHTOA can be used in 3D problems.
What is a plane in geometry?
A plane in geometry is a flat, two-dimensional surface that extends infinitely in all directions.
How can you find the angle between a line and a plane?
Draw a new line from a point on the line creating a right-angled triangle. The angle between the line and the plane is the same as the angle between the initial line and the side of the triangle that lies on the plane.
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 $\frac{\sin (A)}{a} = \frac{\sin (B)}{b} = \frac{\sin (C)}{c}$
This is given in your exam formula booklet.
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 $c$ .
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 $\cos (C) = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$
Where:
- $c$ is the length of the side opposite angle $C$
- $a$ and $b$ are the lengths of the two other sides
This is given in your exam formula booklet.
What type of triangle can the cosine rule be used on?
The cosine rule can be applied to any type of triangle.
Unlike SOHCAHTOA, it is not restricted to right-angled triangles.
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 $c^{2} = a^{2} + b^{2} - 2 a b \cos (C)$
Where:
- $c$ is the length of the side opposite angle $C$
- $a$ and $b$ are the lengths of the two other sides
This is given in your exam formula booklet.
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 the correct angle mode to ensure that it will give you a correct answer. It should be set to radians or degrees depending on the question.
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
This is given in your exam formula booklet.
If $C = 90 °$ $(\frac{π}{2} rad)$ , what does the area formula for a triangle simplify to?
If $C = 90 °$ $(\frac{π}{2} rad)$ , 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 $\sin (90 °) = \sin (\frac{π}{2}) = 1$ .
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.
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.
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.
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.
What is a bearing?
A bearing is a way of describing and using a direction as an angle.
From which compass direction should a bearing always be measured?
A bearing should always be measured from North.
True or False?
Bearings are measured in an anti-clockwise direction.
False.
Bearings are measured in a clockwise direction.
How many figures must a bearing be written with?
A bearing must be written with 3 figures.
For angles under 100°, zero(es) should be used to fill in the missing figures, e.g. 059º, 008º.
True or False?
SOHCAHTOA and Pythagoras' theorem are frequently used in bearings questions.
True.
Pythagoras' theorem and SOHCAHTOA are frequently used in bearings questions.
This is because situations often include finding missing lengths or angles in right-angled triangles.
If a bearing of A from B is known, how do you find the bearing of B from A?
If a bearing of A from B is less than 180^o, then add 180^o to find the bearing of B from A.
E.g. if the bearing of A from B is 030^o, then the bearing of B from A is 210^o.
If a bearing of A from B is greater than 180^o, then subtract 180^o to find the bearing of B from A.
E.g. if the bearing of A from B is 270^o, the bearing of B from A is 090^o.
Which compass direction is indicated by a bearing of 090°?
When a bearing is 090°, it means due east.
True or False?
North should always be indicated on a diagram.
True.
North should always be indicated on a diagram as a point of reference.
What is the angle of elevation?
The angle of elevation is the angle between the horizontal and the line of sight when looking up at an object.
What is the angle of depression?
The angle of depression is the angle between the horizontal and the line of sight when looking down at an object.
Which trigonometric ratio is often used in problems involving angles of elevation and depression?
The trigonometric ratio that is often used in real-life scenarios with angles of elevation and depression is the tangent ratio.
This is because real-life questions are often concerned with the height of an object (the 'opposite' side) and the horizontal distance from an object (the 'adjacent' side).

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