Second Term Lesson Note for Week Eight
Class : JSS 3
Subject : Mathematics
Topic : Trigonometrical ratios of angles
Duration : 40 Minutes
Period : Single Period
Reference Book :
- Essential Mathematics for Junior Secondary School, JSS 3 (Basic 9).
- Lagos State Unified schemes of work for Junior Secondary Schools JSS 1 – 3.
- Online Resources
Instructional Material : Chart showing the trigonometrical ratio functions.
Learning Objectives : By the end of the lesson learners will be able to :
i. Explain trigonometric functions of any given triangles.
ii. Identify the Trigonometrical ratios
iii. Solve problems involving
Content :
THE TRIGONOMETRIC RATIOS
Trigonometry is a measure of ratio of two side of a right angled triangle to the given angles.
There are three trigonometric ratios of angles. These are sine (sin), cosine (cos) and tangent (tan)
Consider the right-angled triangle below
Hypotenuse : the longest side of a right angled triangle. It is denoted by /Hyp/.
Opposite : the side facing the marked or given angle in a right angled triangle. It is denoted by /Opp/.
Adjacent : the third side of the right angled triangle. It is denoted by /Adj/.
Tangent of an Angle
In any right angle triangle,
tangent = Opp/Adj
Example
Use the table of tangent to write down the values of the following (a) tan 36° (b) tan 23.5° (c) tan 45°
Solution
Tan 36°. look for 36° under the column headed x tan 36o = 0.7265
Tan 23.5° look for 23° under the column headed x. then move across until under the column headed 0.5° to find 0.4348 tan 23.5° = 0.4348
Tan 45° = 1
Exercise :
In triangle ABC, Ĉ = 90°, B = 28° and CA = 12cm. Find BC. Give your answer to 2.s.f
SINE AND COSINE OF AN ANGLE
Sine = Opp/ Hyp, Cosine = Adj/ Hyp
The three ratios can be summarized in the word or acronyms as SOH/CAH/TOA
Sin = Opp/ Hyp
Cos = Adj/ Hyp
Tan = Opp/ Adj
Example :
Use tables of sine and cosine to find :
(a) Sin 46.65° (b) cos 15.94°
Solution
Sin 46.65° = 0.7266 (Using the trigonometric table, 46 under 6 difference 5)
(b) Cos 15.94° = 0.9615 ( Using the Cosine table of trigonometry, we check 15 under 9, difference 4)
Exercise :
1. Find the size of an in the triangles below :
2. Given the triangle PQR, the side /PQ/ = 5, side /QR/ = 3. Find :
i. The size of the side /PR/.
ii. The value of Sin Q.
iii. What is the value of Tan P?
Conclusion : At the end of the lesson learners will be able to answer the questions correctly.