Sine and cosine rule Revision MYP 4 - Trigonometry lesson Sine rule - Why do we use the sine rule? What is the sine rule? Exercises with the sine rule
What is it? Used to find size of an angle or length of a side of a triangle with no right angles Two cases: Value of two sides and an angle opposite to one of the sides, or value
of one side and two angles. Vertices have a capital letter, sides have a small one Case 1: Case 2: Sine rule
Exercise (two sides and one angle) B=50.6 to 3sf Your turn! Complete these exercises rounding to 3 s.f. Find the length of b 32m
Find the value of BCA b Find the value of BAC Find the value of BCA and the length of b b
Cosine rule - Why do we need the cosine rule? What is the cosine rule? Activity in groups Cosine rule Used to find length of
a size or value of an angle Used when you cannot have the sine rule (if you do not have the length of a side and the value of an angle opposite to it)
Example 1 Cosine rule Exercise 37cm 42c m B
m c 26 A C Activity Create one question where you need to use the
cosine rule, exchange it with the person next to you and try to solve the exercise Create one question involving the sine rule or the cosine rule, share it with a partner and see if you can solve the others exercise. Ask if you need help!
Remembering trigonometry PYTHAGORAS THEOREM Numerous decades ago the greek mathematician Pythagoras discovered a pattern in relation to right triangles. He found out that if three squares with the same sides lengths as the triangles three different lengths values, positioned on their corresponding edges (sides of the triangle) you would have noticed that the biggest
square achieved was exactly the sum of the two other squares. As you can see in the example a and c added together could possibly make c, and effectively it is like this. This discovery was then transformed into a mathematical formula which is the following one:
The side C, which is the longest one with the biggest area is formally named hypotenuse and is what we are searching to achieve by applying this formula This formula is useful in the case where we know the values of the lengths of two sides of a right triangle and need to discover the third sides value.
Find the value of x: Find the value of ?: INVERSE PYTHAGORAS FORMULAS
If you had the values of c and b and wanted to find the one of a you would have to apply an inverse formula to the Pythagoras theorem. This is the formula: In the case you had to find the value of b the
formula would work exactly the same, with the difference that in the subtraction you have a" at the place of b: Exercises Find the value of the ground: Find the value of h:
RIGHT ANGLED TRIANGLE In a right-angled triangle this is the classification of the sides correlated with the angle "Opposite" is opposite to the angle "Adjacent" is parallel, next to the angle
"Hypotenuse" is the longest oblique side SOHCAHTOA It is used to find either a missing angle or a missing side of a rightangled triangle SOH stands for Sine equals Opposite over Hypotenuse
CAH stands for Cosine equals Adjacent over Hypotenuse TOA stands for Tangent equals Opposite over Adjacent Therefore: if we have to find an angle
We must use the values of the opposite and adjacent to find it Opposite/adjacent: TAN Tan (theta) = Opposite/adjacent Inverse tan (Opposite/adjacent)= theta
EXERCISES Question N1 Find the length of side b if side c is 38 m and angle A is 48 MORE EXERCISES Question N2 Use tangent to find side x
Sources http://m4ths.com/web_documents/50_free_response_sine_rule _problems_-_steve_blades_worksheet.pdf http://www.cimt.org.uk/projects/mepres/step-up/sect4/index.h tm
http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/fu rthertrigonometryhirev1.shtml http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/fu rthertrigonometryhirev2.shtml http://www.mathcentre.ac.uk/resources/Engineering%20math s%20first%20aid%20kit/latexsource%20and%20diagrams/4_6
.pdf http://locusacademy.org/sine-and-cosine-rule/