True or False? Using the other acute angle in the same triangle swaps the opposite and adjacent sides.

True. The opposite and adjacent are named relative to the angle you choose, so they exchange roles. The hypotenuse is unaffected, because it is fixed by the right angle rather than by your choice of angle.

How do you decide which trigonometric ratio to use to find a missing length?

Label the sides, then choose the ratio that uses the side you know and the side you want. Substitute the values, keeping brackets around the angle, then rearrange to make the unknown length the subject.

When finding an angle, how do you choose which trigonometric ratio to use?

Look at which two sides you have been given, then pick the ratio built from those two. Here both lengths are known and the angle is the unknown, which is the reverse of the situation when you are finding a length.

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Trigonometry (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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FrontTrigonometry to Find Lengths
In a right-angled triangle, how do you label the three sides for trigonometry?

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Cards in this collection (12)

In a right-angled triangle, how do you label the three sides for trigonometry?
Label them relative to the angle you are using, often marked $θ$ .
The opposite is the side across from that angle, the adjacent is the side next to it, and the remaining side is the hypotenuse.
What does SOHCAHTOA stand for?
It packs the three ratios into one word: $sin θ = \frac{O}{H}$ , $cos θ = \frac{A}{H}$ and $tan θ = \frac{O}{A}$ .
Each group of three letters gives one ratio, with the first letter naming the function and the other two naming the fraction.
True or False?
Using the other acute angle in the same triangle swaps the opposite and adjacent sides.
True.
The opposite and adjacent are named relative to the angle you choose, so they exchange roles.
The hypotenuse is unaffected, because it is fixed by the right angle rather than by your choice of angle.
How do you decide which trigonometric ratio to use to find a missing length?
Label the sides, then choose the ratio that uses the side you know and the side you want.
Substitute the values, keeping brackets around the angle, then rearrange to make the unknown length the subject.
A right-angled triangle has an angle of 43°, with the opposite side $x$ and the adjacent side 9 cm. Complete the working:
$tan (43) = \frac{x}{9}$ , so $x = 9 \times______=______$ cm
The completed working is:
$x = 9 \times tan (43) = 8.39$ cm
The unknown sits on top of the fraction, so multiplying both sides by 9 releases it, and the answer is given to 3 significant figures.
True or False?
These trigonometric ratios work in any triangle.
False.
The ratios $sin$ , $cos$ and $tan$ apply only to right-angled triangles.
Without a right angle there is no hypotenuse for the other two sides to be measured against.
When finding an angle, how do you choose which trigonometric ratio to use?
Look at which two sides you have been given, then pick the ratio built from those two.
Here both lengths are known and the angle is the unknown, which is the reverse of the situation when you are finding a length.
How do you get from $cos y = \frac{8}{23}$ to the angle $y$ ?
Apply the inverse cosine, written ${cos}^{- 1}$ .
So $y = {cos}^{- 1} (\frac{8}{23})$ , which gives 69.6° to 1 decimal place.
Where do you find the inverse trigonometric functions on a calculator?
Above the $sin$ , $cos$ and $tan$ keys, reached using the shift key.
They are labelled ${sin}^{- 1}$ , ${cos}^{- 1}$ and ${tan}^{- 1}$ .
Complete the two rounding conventions by filling in the missing numbers:
A missing length is given to $______$ significant figures unless you are told otherwise.
A missing angle is given to $______$ decimal place unless you are told otherwise.
The completed conventions are:
A missing length is given to 3 significant figures unless you are told otherwise.
A missing angle is given to 1 decimal place unless you are told otherwise.
True or False?
You can find an angle using $tan$ if you know the hypotenuse and the opposite side.
False.
$tan$ is built from the opposite and the adjacent, so those are the two sides it needs.
Given the opposite and the hypotenuse you would use $sin$ instead.
A right-angled triangle has an opposite side of 5 cm and an adjacent side of 12 cm. Which calculation gives the angle?
Take the inverse tangent of $\frac{5}{12}$ , because the opposite and the adjacent are the two sides you have.
That is ${tan}^{- 1} (\frac{5}{12})$ , giving an angle of 22.6° to 1 decimal place.

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