Title MATHEMATICS FOR PHYSICS.pdf ✅

CLASS VIII PHYSICS Trigonometric Ratios Introduction to Trigonometry: The word 'trigonometry' is derived from the Greek roots --- 'tri' meaning 'three'; 'gonia' meaning 'an angle', 'met- ron' meaning 'measure'. Thus 'trigonometry' means three angle measure. It is an analytical study of a three an- gled geometric figure, namely the triangle. Note: While measuring angles right hand screw rule is employed. Trigonometrical Ratios: In right triangle OPM, if ∠POM = θ, then the side MP (perpendicular) is called the opposite side ; the longest side OP is called the hypotenuse and the third side OM is called the Adjacent side (base) of the triangle. (i) Sine of angle θ, written as sin θ = MP OP = Opposite side Hypotenuse side (ii) Cosine of angle θ, written as cos θ = OM OP = Adjacent side Hypotenuseside (iii) Tangent of angle θ, written as tan θ = MP OM = Opposite side Adjacent side (iv) Cotangent of angle θ, written as cot θ = OM MP = Adjacent side Opposite side (v) Secant of angle θ, written as sec θ = OP OM = Hypotenuse side Adjacent side (vi) Cosecant of angle θ, written as cosec θ = OP MP = Hypotenuse side Opposite side Note: i) From the above relations, we can say that sin θ = 1/cosec θ or cos θ = 1/sec θ ii) According to Pythagoras theorem, ( Hypotenuse side ) 2 = ( Adjacent side ) 2 + ( Opposite side ) 2 Table for the values of Trigonometric ratios of some standard angles : √ 0 4 √ 1 4 √ 2 4 √ 3 4 √ 4 4 0 ∘ 30∘ 45∘ 60∘ 90∘ MATHEMATICS FOR PHYSICS SYNOPSIS - 1