Lesson Notes By Weeks and Term - Junior Secondary School 3
TRIGNOMETRICAL RATIO
TRIGNOMETRICAL RATIO
SUBJECT: MATHEMATICS
CLASS: JSS 3
DATE:
TERM: 2nd TERM
TOPIC: TRIGNOMETRICAL RATIO Trignometrical ratio is a ratio of the lengths of two sides of a right-angle triangle. The three trignometrical ratios are sine (sin) cosine (cos) and tangent (tan). The word tri- means three, thus trignometrical ratio deals with three sided figure (triangle). In a right-angled triangle, the longest side is called the hypotenuse (opp the right angle), the side adjacent (next) to the given angle is called the Adjacent while the side opposite to the given angle is called the opposite. B B Opposite hypotenuse Adj hyp Fig 1 Fig 2 A opp C A Adjacent C Note: To be able to know the ratio easily take note of the acronym SOHCAHTOA. Where S stands for sine, C stands for cosine, and T for tangent. Degree and Minutes Angles are often measured to the nearest degree. In some state, degree may be subdivided into minutes and. Note: 10 =60 minutes. This is written as 60/. To change from minutes to degree, we divide the number by 60. Example: convert 100 to minutes Solution: 10 x 60 = 600mins EVALUATION: SINE OF ANGLE In a right-angle triangle, the ratio of opposite to hypotenuse is defined as the sine of the angle under consideration. From fig 1, sin ø = AB/BC. The ratio does not depend on the size of the triangle but depends only on the size of the angle (ø). To find sine of the angles, we use of either calculator or the sine table. In use of sine table, since the sine of angle increases as the angle increases, thus the differences will be added. EVALUATION use mathematical table to find USE OF SINE IN SOLVING TRIANGLES Example: Find the marked side or the angle in each of the following. Give your answer to 2.s.f.g. 4cm Fig 1 x 15cm 46 ø 9cm Fig 2 Solution: From Fig 2 From fig 1 sinø = opp/hyp Sin46 = 15/x sinø =4cm/9cm X=15/sin46 sinø = 0.444 X = 15/0.7193 ø = sin1 0.4444 X=20.85, X=21 (2.s.f.g) ø = 26.49, ø= 26 (2.s.f.g) EVALUATION What is value of X and ø in the below triangle 28 x ø 10 COSINE OF ANGLES In a right angled triangle, the ratio of adj/hyp is defined as the of angle under consideration. Using diagram: ø adj hyp opp Thus Ó¨ = AB/AC This value of the ratio does not depend on the size of triangle but on the size of angle. CALCULATIONS OF COSINE OF ANGLES Find the unknown side or angle in the below triangles 2 5cm ø ø 3.5cm 1 solution: 2 5cm ø ø cosø = Adj/hyp cosø = adj/hyp cosø = ½ cosø = 3.5cm/ 5cm ø = cos1 0.5 ø = cos1 0.7 ø = 600 ø = 45.67 TANGENT OF ANGLES The tangent of any angle is the ratio opp/adjacent. In short form, tanÓ¨ = opp/adj CALCULATING TANGENT OF TRIANGLES Examples: find the side of the triangle marked x. correct to 2 S.F.G in the figure below. 40 8cm hyp opp xcm solution: tan ø = opp/adj = xcm/8cm tan ø = x/8, ø = tan 40 x 8 ø = 0.8391x8 ø = 6.7128; ø = 6.7( 2 s.f.g) EVALUATION: calculate the side of the triangle marked x 60 19cm (i) (ii) 75 5 x x READING ASSIGNMENT Essential mathematics for J.S.S 3 Pg 101-116 Exam Focus for J.S.C.E. for J.S.S 3 Pg 224-235 WEEKEND ASSIGNMENT Calculate the side marked P,Q, and α Draw: x 5 q 30 p THEORY x 16cm 7 A 20cm 60cm B 45 C 35cm
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