Sin 30

How to find the values? To learn the table, we should first know how We know that • tan θ = sin θ/cosθ • sec θ = 1/cos θ • cosec θ = 1/sin θ • cot θ = 1/cot θ Now let us discuss different values For sin For memorising sin 0°, sin 30°, sin 45°, sin 60° and sin 90° We should learn it like • sin 0° = 0 • sin 30° = 1/2 • sin 45° = 1/√2 • sin 60° = √3/2 • sin 90° = 1 So, our pattern will be like 0, 1/2, 1/√2, √3/2, 1 For cos For memorising cos 0°, cos 30°, cos 45°, cos 60° and cos 90° Cos is the opposite of sin. We should learn it like • cos 0° = sin 90° = 1 • cos 30° = sin 60° = √3/2 • cos 45° = sin 45° = 1/√2 • cos 60° = sin 30° = 1/2 • cos 90° = sin 0° = 0 So, for cos, it will be like 1, √3/2, 1/√2, 1/2, 0 -ad- For tan We know that tan θ = sin θ /cos θ So, it will be • tan 0° = sin 0° / cos 0° = 0/1 = 0 • tan 30° = sin 30° / cos 30° = (1/2)/ (√3/2) = 1/√3 • tan 45° = sin 45° / cos 45° = (1/√2)/ (1/√2) = 1 • tan 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3 • tan 90° = sin 90° / cos 90° = 1/0 = Not Defined = ∞ So, for tan, it is 0, 1/√3, 1, √3, ∞ -ad- For cosec We know that cosec θ = 1/sin θ For sin, we know 0, 1/2, 1/√2, √3/2, 1 So, for cosec it will be • cosec 0° = 1 / sin 0° = 1/0 = Not Defined = ∞ • cosec 30° = 1 / sin 40° = 1/(1/2) = 2 • cosec 45° = 1 / sin 45° = 1/(1/√2) = √2 • cosec 60° = 1 / sin 60° = 1/(√3/2) = 2/√3 • cosec 90° = 1 / sin 90° = 1/1 = 1 So, for cosec, it is ∞, 2, √2, 2/√3, 1 -ad- For sec We know that sec θ = 1/cos θ For cos, we know 1, √3/2, 1/√2, 1/2,...

Adjacent is always next to the angle And Opposite is opposite the angle Sine, Cosine and Tangent Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same no matter how big or small the triangle is To calculate them: Divide the length of one side by another side Example: What is the sine of 35°? Usingthistriangle(lengthsare only to one decimal place): sin(35°) = Opposite Hypotenuse = 2.8 4.9 = 0.57... cos(35°) = Adjacent Hypotenuse = 4.0 4.9 = 0.82... tan(35°) = Opposite Adjacent = 2.8 4.0 = 0.70... Size Does Not Matter The triangle can be large or small and the ratio of sides stays the same. Only the angle changes the ratio. Try dragging point "A" to change the angle and point "B" to change the size:

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How to find the values? To learn the table, we should first know how We know that • tan θ = sin θ/cosθ • sec θ = 1/cos θ • cosec θ = 1/sin θ • cot θ = 1/cot θ Now let us discuss different values For sin For memorising sin 0°, sin 30°, sin 45°, sin 60° and sin 90° We should learn it like • sin 0° = 0 • sin 30° = 1/2 • sin 45° = 1/√2 • sin 60° = √3/2 • sin 90° = 1 So, our pattern will be like 0, 1/2, 1/√2, √3/2, 1 For cos For memorising cos 0°, cos 30°, cos 45°, cos 60° and cos 90° Cos is the opposite of sin. We should learn it like • cos 0° = sin 90° = 1 • cos 30° = sin 60° = √3/2 • cos 45° = sin 45° = 1/√2 • cos 60° = sin 30° = 1/2 • cos 90° = sin 0° = 0 So, for cos, it will be like 1, √3/2, 1/√2, 1/2, 0 -ad- For tan We know that tan θ = sin θ /cos θ So, it will be • tan 0° = sin 0° / cos 0° = 0/1 = 0 • tan 30° = sin 30° / cos 30° = (1/2)/ (√3/2) = 1/√3 • tan 45° = sin 45° / cos 45° = (1/√2)/ (1/√2) = 1 • tan 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3 • tan 90° = sin 90° / cos 90° = 1/0 = Not Defined = ∞ So, for tan, it is 0, 1/√3, 1, √3, ∞ -ad- For cosec We know that cosec θ = 1/sin θ For sin, we know 0, 1/2, 1/√2, √3/2, 1 So, for cosec it will be • cosec 0° = 1 / sin 0° = 1/0 = Not Defined = ∞ • cosec 30° = 1 / sin 40° = 1/(1/2) = 2 • cosec 45° = 1 / sin 45° = 1/(1/√2) = √2 • cosec 60° = 1 / sin 60° = 1/(√3/2) = 2/√3 • cosec 90° = 1 / sin 90° = 1/1 = 1 So, for cosec, it is ∞, 2, √2, 2/√3, 1 -ad- For sec We know that sec θ = 1/cos θ For cos, we know 1, √3/2, 1/√2, 1/2,...

Adjacent is always next to the angle And Opposite is opposite the angle Sine, Cosine and Tangent Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same no matter how big or small the triangle is To calculate them: Divide the length of one side by another side Example: What is the sine of 35°? Usingthistriangle(lengthsare only to one decimal place): sin(35°) = Opposite Hypotenuse = 2.8 4.9 = 0.57... cos(35°) = Adjacent Hypotenuse = 4.0 4.9 = 0.82... tan(35°) = Opposite Adjacent = 2.8 4.0 = 0.70... Size Does Not Matter The triangle can be large or small and the ratio of sides stays the same. Only the angle changes the ratio. Try dragging point "A" to change the angle and point "B" to change the size:

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle', and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it.