Back to: MATHEMATICS JSS3
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In today’s Mathematics class, We will be talking about Trigonometry. We hope you enjoy the class!
TRIGNOMETRICAL RATIO
The trigonometrical ratio is a ratio of the lengths of two sides of a rightangle triangle. The three trigonometrical ratios are sine (sin) cosine (cos) and tangent (tan). The word tri means three, thus trigonometrical ratio deals with threesided figure (triangle).
In a rightangled 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.
Note: To be able to know the ratio easily take note of the acronym SOHCAHTOA.
Where S stands for sine, C stands for cosine, T for Tangent, O for Opposite, H for Hypotenuse and A for Adjacent.
Degree and Minutes
Angles are often measured to the nearest degree. In some situations, degrees may be subdivided into minutes.
Note:
1^{0} =60 minutes. This is written as 60^{/}.
To change from minutes to degrees, we divide the number by 60.
Example: convert 10^{0} to minutes
Solution: 10 x 60 = 600mins
EVALUATION:
 Convert the following to minutes: A. 16^{0} B. 50^{0}
 Rewrite and give your answer in degree to 1.dp A. 46^{0} 15^{1} B. 39^{0} 25^{1} C. 140^{0} 4
SINE OF ANGLE
In a rightangled triangle, the ratio of the opposite to hypotenuse is defined as the sine of the angle under consideration. this can be easily remembered using SOHCAHTOA.
SOH here means Sine = $\frac{Opposite}{Hypotenuse}$
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 the sine of the angles, we use either a calculator or the sine table. In the use of sine table, since the sine of angle increases as the angle increases, thus the differences will be added.
EVALUATION
Use a mathematical table to find
 sin 43
 sin 14.58
 sin 30.6
USE OF SINE IN SOLVING TRIANGLES
Example:
Find the marked side of the angle in each of the following. Give your answer to 2.s.f.g.
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 = sin^{1} 0.4444
X=20.85, X=21 (2.s.f.g) ø = 26.49, ø= 26 (2.s.f.g)
EVALUATION
What is the value of X and ø in the below triangle
COSINE OF ANGLES
In a rightangled triangle, the ratio of adj/hyp is defined as the angle under consideration.
this can be easily remembered using SOHCAHTOA.
CAH here means Cosine = $\frac{Adjacent}{Hypotenuse}$
Using diagram:
Thus Ө = AB/AC
This value of the ratio does not depend on the size of the triangle but on the size of the angle.
CALCULATIONS OF COSINE OF ANGLES
Find the unknown side or angle in the below triangles
cosø = Adj/hyp cosø = adj/hyp
cosø = ½ cosø = 3.5cm/ 5cm
ø = cos^{1} 0.5 ø = cos^{1} 0.7
ø = 60^{0} ø = 45.67
TANGENT OF ANGLES
The tangent of any angle is the ratio opp/adjacent.
this can be easily remembered using SOHCAHTOA.
TOA here means Tangent = $\frac{Opposite}{Adjacent}$
In short form, tanӨ = 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.
solution:
tan ø = opp/adj = xcm/8cm
tan ø = x/8, ø = tan 40 x 8
ø = 0.8391×8
ø = 6.7128; ø = 6.7( 2 s.f.g)
EVALUATION: calculate the side of the triangle marked x
READING ASSIGNMENT
Essential mathematics for J.S.S 3 Pg 101116
Exam Focus for J.S.C.E. for J.S.S 3 Pg 224235
WEEKEND ASSIGNMENT
 Convert 32.4^{0} to degree and minutes. A. 32 42^{ 1 } 32 44^{1} C. 32 24^{1}
 Cos 60 is equal to —— A. 0.5 B. 0.49 C. 1/25
 Calculate the side marked P, Q, and α


 the value of P is 9.6 B. 8.7 C. 10
 the value of q is — A. 10 B. 8 C. 13
 the value of α is —A. 45 B.60 C. 30

Theory
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In our next class, we will be talking about “Angles of Elevation and Depression”. We are very much eager to meet you there.
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