Trigonometry notes
47 notes by 41 users · Page 1 of 2
This Trigonometry notes page gathers over 30 user-made notes, covering ratios, graphs, radians and identities. The collection is mainly school-level: school students can practise ratios and triangle rules, while teachers can find material on those topics. Pick a note to start revising.
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- Pythagorean Theorem16
- Trigonometric Ratios and Right Triangles105
- Radians and Circular Measure17
- Unit Circle28
- Exact Trigonometric Values26
- Trigonometric Functions and Graphs44
- Sine and Cosine Rules65
- Applications of Trigonometry6
- Trigonometric Identities94
- Angle Sum and Double Angle Formulas13
- Trigonometric Equations8
Notes
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2D geometry
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Sine Rule The sine rule is a trigonometric rule which is true for all triangles. The sine rule states that, in the above triangle abc: SinA = SinB = SinC a b c &nbs...
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Tangent and the graph of tan(x) In a right-angled triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. tan(x) = O = Sin(x)  ...
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Sine & the graph of sin(x) In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Sin(X) = O H For...
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Radians Radians are a measure of angular rotation, similar to degrees. Unlike degrees, radians are a real number, and do not have a unit. An angle is said to be 1 radian if the length of the arc it makes on a circles ci...
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Triginometry You can find the area of any triangle using: area = 1/2bcsin A or area = 1/2acsin B or area = 1/2absin C Radians, arcs, and sectors Arc length of sector = radius x central angle Area of sector = (central angle x radiu...
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TRIG 1. it is always finding a missing side of a right angle triangle, but only lable TWO sides.2.it is impossible to do unless they give you an angle!3. the three worst words in maths are sin, cos and tan4. SOHCAHTOA (see...
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Cosine Rule The Cosine rule, similar to the sine rule, is true for all triangles. The Cosine rule states that, in any triangle abc, This is rule is useful when:
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random maths bits to remember in SOH CAH TOAwhat is up goes down... Angle lines New Page
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Unit Circle reference angle General formula (θ+360v)° 32+ 180=
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Maths - Trigonometry and Bearings Area of a triangle: To be able to calculate the area of a triangle, you need to know two sides and its included angle. Example: Find the area of triangle ABC. The sine rule: We can use the sine rule when we're given t...
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Trigonometry
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8.4 - 8.5 Notes 8.4- Sine, Cosine, and TangentSohCahToaSine Cosine Tangent Opposite Leg Adjacent Leg Opposite Leg Hypotenuse Hypotenuse Adjacent LegSin(A)=a/c Sin(B)=b/cCos(A)=b/c Cos(B)=a/cTan(A)=a/b Tan(B)=b/aPropertiesSin(A)=Cos(B...
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Table of Trigonometric Identities Reciprocal identitiesPythagorean IdentitiesQuotient IdentitiesCo-Function IdentitiesEven-Odd IdentitiesSum-Difference FormulasDouble Angle FormulasPower-Reducing/Half Angle FormulasSum-to-Product FormulasProduct-to-Su...
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Trigonometry notes
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SOH CAH TOA SOH CAH TOA Find angle C. Give your answer correct to 1 dp. Answer We have been given the lengths of AC and BC and asked to find angle C. AC is adjacent to angle C. BC is the hypotenuse. So we use the formula: cos = a...
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Trigonometric Identities Trigonometric identities are formulae that exist between the trigonometric functions. They are useful for solving algebraic problems involving trigonometric functions. Here is a list of some common trigonometric ident...
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Cosine and the graph of cos(x) In a right-angled triangle, the cosine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Cos(X) = A H For exa...
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Untitled Unit 6 : Trigonometric Functions Jocelyn Bassel Identify the basic curve: y=sin0 or y=cos0 Factor out k from the brackets, if necessary. Label the horizontal axis in degrees or radians, as appropriate. Recommended: Dr...
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5.1 Trigonometric Ratios of Acute angels - created from Mind Map SOH CAH TOA can only be applied to right angled triangles How to solve 1) The sum of the interior angles of any triangle is 180* An acute are less than 90*. A right triangle will have acute angles that are complementa...
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Relations between angles and sides - created from Mind Map use cosine law Area expressed in terms of sides and angles p=semiperimeter=(a+b+c)/2
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PFP Mathematics PFP Mathematics 2 1. TRIGONOMETRY 1.1 Angles, Arcs and Sectors Angles An angle is determined by rotating a ray (half-line) about its endpoint. The initial side of an angle is the starting position of the ray. The term...
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Trigonometry Trigonometry Sine= oppositehypotenuse
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Geometric Reasoning Trigonometry Finding an unknown side If the unknown side is at the top of the fraction in the equation (sin = o/h. o is on the top), then you multiply it together with the equation being 'h sin(angle)' or 'h x sin(ang...
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Trignometry
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Trigonometry - created from Mind Map Pythagorean Theorem Pythagoras was a Greek mathematician His theorem was: a² + b² = c² Trigonometric Functions Soh Cah Toa Sine Cosine Tangent sin(θ) = O ÷ H θ = sin⁻¹(O ÷ H) cos(θ) = A ÷ H θ = cos⁻¹(A ÷ H) tan(θ) = O...
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Area of triangles NOTES: FINDING THE AREA OF ANY TRIANGLE Use the formula 1/2 ab sin c You use this when you don't know the perpendicular height of the triangle label the sides A,B,C Substitute the values into the fo...
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How to solve: Trigonometry How to solve: When solving trigonometry questions, you should label the three different sides: the hypotenuse, opposite and the adjacent. The hypotenuse is the longest side, the opposite is the side opposite the label...
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Untitled Maths studyTrigonometry TRIANGLES If I DON'T have a right angle Heron's forumla Sine (ANY TRIANGLE) Cosine CIRCLES Circumference = pi D or 2 pi r Area = pi r squared If I DO have a right angleSOHCAHTOAPhythagoras' The...
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Sine rule sin= opp/hyptTan= opp/hyptcos= adj/hypREMEMBER: Some Old Hulk Carries A Huge Tub Of Ale a/sinA=b/sinB=c/sinCexampleA=118 degrees B= 39 degreesb=7cma X sin 39 degrees = 7cm X sin 118 degrees a X sin 39/ sin 39 (sin 39 ...
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CIRCULAR MEASURE - created from Mind Map Converting units Length of Arc Shaded Segment
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Beggining Trigonometry Q: With the information given to you, find out what A and B equal.A: A= B= Steps: Find out if you use a sine, tangent,or cosine. When you figure that out, write ...
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SOHCAHTOA Sine=opposite/hypotenuseCos=adjacent/hypotenuseTan=opposite/adjacentPythagorean theorem= a squared+b squared=c squaredUse special triangles to find missing sides45-45-90: n,n, hypotenuse: n root 330-60-90: short side:...
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Untitled There are many ways. I just use one for instance: tg(35.8)=AB/BD ~0.72=AB/(BC+20) Another time: tg(50.5)=AB/BC ~1.21=AB/BC So : (0.72)(BC+20)=(1.21)(BC) And BC=29.38 Now AC=BC/cos(50.5) Therefore AC=46.19
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Sinusodial - created from Mind Map Key Points on f(x) Increasing interval & Decreasing interval Period
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Mathematics B Revision Radian Measure 90 degrees = pi/2 180 degrees = pi 270 degrees = 3pi/2 360 degrees = 2pi theta radians = theta degrees x pi/180 or theta degrees = theta radians x 180/pi Exact Trig Values
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AS MATHS
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Trig Review Trig Review Sin= O/H Opposite / Hypotenuse Cos= A/H Adjacent / Hypotenuse Tan= O/A Opposite / Adjacent
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Maths Maths Test: Trigonometry (SOHCAHTOA), Pythagoras ,3D Trigonometry & Pythagoras, Graphs of Trigonometry Function, Sine Rule/Cosine Rule/Sneaky,Ambiguous ) Trigonometry: SOHCAHTOASOHSin A=
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TRIGONOMETRY - created from Mind Map SOH CAH TOA opposite over hypotenuse adjacent over hypotenuse Opposite over adjacent Rules SINE RULE COSINE RULE TRIGONOMETRY
More Trigonometry resources
About trigonometry notes
GoConqr OriginalUsing trigonometry notes
For a starting point, Sine & the graph of sin(x) introduces the sine ratio in a right-angled triangle. The notes on cosine and tangent cover their corresponding ratios and graphs. Read these alongside one another if you want to compare the functions.
For triangle problems, the Sine Rule and Cosine Rule notes explain when each rule is useful. The notes on trigonometry and bearings also cover triangle area and the sine rule.
Build a revision route
Choose a note that matches the part you are studying, then write down the key relationships in your own words. Return to the notes on Radians when working with angular measure, or use Table of Trigonometric Identities to review different groups of identities.
When you want to check what you remember, switch to a quiz on the unit page. Flashcards can help you revisit key terms and formulae. Choose a note and begin with the topic you want to practise.
Frequently asked questions
Which note is a useful place to start?
Sine & the graph of sin(x) is a useful starting point for reviewing a ratio in a right-angled triangle. It introduces sine using the opposite side and hypotenuse. The notes on cosine and tangent then offer related material on those ratios and their graphs.
What topics do these notes cover?
The collection includes notes on sine, cosine and tangent, as well as radians and triangle rules. Other notes cover bearings, triangle area and trigonometric identities. You can choose a specific topic rather than reading the collection in a fixed order.
Are the notes free to use?
Yes. Every note listed here is free to open and study without an account. The resources were made by GoConqr users, not by GoConqr. A free account also lets you save quiz scores and make your own notes, quizzes, mind maps and flashcards.