Sine and cosine rule Revision MYP 4 Trigonometry

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 3 sf

Your turn! – Complete these exercises rounding to 3 s. f. Find the length of b Find the value of BCA 32 m 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 42 cm B A 37 cm m c 26 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 other’s 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 triangle’s 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 side’s 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 θ • "Adjacent" is parallel, next to the angle θ • "Hypotenuse" is the longest oblique side

SOHCAHTOA • It is used to find either a missing angle or a missing side of a right– angled 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 N° 1 • Find the length of side b if side c is 38 m and angle A is 48°

MORE EXERCISES Question N° 2 • Use tangent to find side x

Sources • http: //m 4 ths. com/web_documents/50_free_response_sine_rule_proble ms_-_steve_blades_worksheet. pdf • http: //www. cimt. org. uk/projects/mepres/step-up/sect 4/index. htm • http: //www. bbc. co. uk/schools/gcsebitesize/maths/geometry/furthertrigo nometryhirev 1. shtml • http: //www. bbc. co. uk/schools/gcsebitesize/maths/geometry/furthertrigo nometryhirev 2. shtml • http: //www. mathcentre. ac. uk/resources/Engineering%20 maths%20 first %20 aid%20 kit/latexsource%20 and%20 diagrams/4_6. pdf • http: //locusacademy. org/sine-and-cosine-rule/