The perfect study guide for understanding trigonometry for your IGCSE exams or any other exams in general. The notes consists of examples, diagrams, practice questions, and answers, as well as tips to make it is easy for you to learn and understand. It covers all corners of trigonometry to make sur...
Complete Math TRIGONOMETRY
IGCSE NOTES (Updated Syllabus
Version)
What are trigonometric ratios?
Trigonometry is a branch of mathematics that deals with the relationships
between the sides and angles of triangles, particularly right-angled triangles.
It is important because it has practical applications in fields such as
engineering, physics and architecture. In these fields, understanding the
properties of right-angled triangles is necessary for solving problems
involving angles, distances and forces. Additionally, trigonometric ratios are
useful for understanding and solving problems in navigation, astronomy and
surveying.
Trigonometry has been a crucial tool in the field of astronomy since ancient
times, enabling astronomers to determine the distances between stars and
planets. Today, NASA scientists rely on these mathematical techniques to
design and launch space shuttles and rockets. Without this knowledge,
humans would not have been able to explore the Moon or launch satellites
into space. The Solar System has captivated human beings throughout
history, and right-angle trigonometry has played a key role in unlocking its
mysteries and enabling us to achieve extraordinary feats in space exploration.
Trigonometry
Trigonometry is a topic within mathematics that can be used to calculate
angles and lengths in triangles.
The sides of a right-angled triangle
Your first step in solving a trigonometry problem should be to draw a
diagram and label the side lengths.
,One of the angles in the right-angled triangle (not the \(90^\circ\) angle)
needs to be labelled or given a value to allow you to label the side lengths.
The Greek letter \(\theta\) (pronounced 'theta') is often used to label one of
the angles.
The longest side (opposite the right angle) is known as the hypotenuse.
The side that is opposite the labelled angle, \(\theta\), is known as the
opposite angle.
The side that is next to the labelled angle, \(\theta\), is known as the adjacent
angle.
1) Draw this right-angled triangle and label the sides.
,2) Draw this right-angled triangle and label the sides.
The three trigonometric ratios
Look at this right-angled triangle. The lengths of the sides are all known and
labelled.
, You can work out the ratios between different sides like this:
Ratio of the opposite side to the hypotenuse \(= 6\div 10 = 0.6\).
Ratio of the adjacent side to the hypotenuse \(= 8\div 10 = 0.8\).
Ratio of the opposite side to the adjacent side \(= 6\div 8 = 0.75\).
What if you have a triangle with different side lengths but the same angles as
the one above? What will this mean about the ratios of the sides?
Ratio of the opposite side to the hypotenuse \(= 3\div 5 = 0.6\).
Ratio of the adjacent side to the hypotenuse \(= 4\div 5 = 0.8\).
Ratio of the opposite side to the adjacent side \(= 3\div 4 = 0.75\).
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller mandyigcse93. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $0.01. You're not tied to anything after your purchase.
