Trigonometric Values (0°, 30°, 45°, 60°, 90°)

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• Trigonometric Values (0°, 30°, 45°, 60°, 90°)

Angle (θ): 0° | 30° | 45° | 60° | 90°

       sin θ: 0 | 1/2 | 1/√2 | √3/2 | 1

       cos θ: 1 | √3/2 | 1/√2 | 1/2 | 0

       tan θ: 0 | 1/√3    | 1   |  √3 | Not Defined (∞)

Easy Memory Trick

• SIN (Increasing): 0 → 1 → 2 → 3 → 4 (√0/2, √1/2, √2/2, √3/2, √4/2 )​​​


• COS (Decreasing): 4 → 3 → 2 → 1 → 0 (√4/2, √3/2, √2/2, √1/2, √0/2)​​


• TAN = SIN ÷ COS

Angle: 0° → 30° → 45° → 60° → 90°

 tan θ: 0 → 1/√3 → 1   →  √3 → Not Defined (∞)

Formula to Remember

• SIN: 0 → 1 → 2 → 3 → 4 → √ → ÷2


• COS: 4 → 3 → 2 → 1 → 0 → √ → ÷2


• TAN = SIN ÷ COS

Memory Sentence: "SIN goes Up, COS comes Down, TAN divides them Around."

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Trigonometric Table Trick (0°, 30°, 45°, 60°, 90°)

1st: Remember the numbers : 0 → 1 → 2 → 3 → 4

2nd: SIN Trick

Take the square root of each number and divide by 2.

• 0° = √0/2 = 0


• 30° = √1/2 = 1/2


• 45° = √2/2 = 1/√2


• 60° = √3/2


• 90° = √4/2 = 1

Memory: SIN = 0 → 1 → 2 → 3 → 4 (√ and ÷2)

3rd: COS Trick

Write the same numbers in reverse. : 4 → 3 → 2 → 1 → 0

Take the square root and divide by 2.

• 0° = √4/2 = 1


• 30° = √3/2


• 45° = √2/2 = 1/√2


• 60° = √1/2 = 1/2


• 90° = √0/2 = 0

Memory: COS = 4 → 3 → 2 → 1 → 0 (√ and ÷2)

4th: TAN Trick

TAN = SIN ÷ COS

So remember only this: 0 → 1/√3 → 1 → √3 → ∞

Final Memory Chart

Angles: 0° → 30° → 45° → 60° → 90°

SIN: √0/2 → √1/2 → √2/2 → √3/2 → √4/2

COS: √4/2 → √3/2 → √2/2 → √1/2 → √0/2

TAN: 0 → 1/√3 → 1 → √3 → ∞

Golden Rule : i. SIN goes UP,  ii. COS comes DOWN,  iii. TAN = SIN ÷ COS

Easy Trick

1. TAN and COT are reciprocals

• cot θ = 1 / tan θ

TAN: 0 → 1/√3 → 1 → √3 → ∞

COT: ∞ → √3 → 1 → 1/√3 → 0

2. COS and SEC are reciprocals

• sec θ = 1 / cos θ

COS: 1 → √3/2 → 1/√2 → 1/2 → 0

SEC: 1 → 2/√3 → √2 → 2 → ∞

3. SIN and COSEC are reciprocals

• cosec θ = 1 / sin θ

SIN: 0 → 1/2 → 1/√2 → √3/2 → 1

COSEC: ∞ → 2 → √2 → 2/√3 → 1

Golden Memory Rule

• SIN ↔ COSEC (Reciprocals) এটাৰ বিপৰীত মান


• COS ↔ SEC (Reciprocals) এটাৰ বিপৰীত মান 


• TAN ↔ COT (Reciprocals) এটাৰ বিপৰীত মান

Just memorize SIN, COS, and TAN. Then get the remaining three by taking the reciprocal (1/value). This is the easiest way to remember all six trigonometric functions. ("প্ৰথমে SIN, COS আৰু TAN মুখস্থ কৰক। তাৰ পিছত COSEC, SEC আৰু COT সহজে পাব—কেৱল বিপৰীত মান (Reciprocal) ল'লেই হ'ব।")

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Trigonometric Values – Easy Memory Trick (সহজে মনত ৰখাৰ কৌশল)

1. SIN (Sine / ছাইন)

Remember the numbers: 0 → 1 → 2 → 3 → 4 (Take the square root (√) of each number and divide by 2.)

0 → 1 → 2 → 3 → 4 সংখ্যাবোৰ মনত ৰাখক। প্ৰতিটো সংখ্যাৰ বৰ্গমূল (√) লওক আৰু ২-এ ভাগ কৰক।

SIN Values: √0/2 → √1/2 → √2/2 → √3/2 → √4/2

2. COS (Cosine / কছাইন)

Reverse the SIN order: 4 → 3 → 2 → 1 → 0 (Take the square root (√) and divide by 2.)

SIN-ৰ ক্ৰমটো ওলোটাই লিখক: 4 → 3 → 2 → 1 → 0। তাৰ পিছত প্ৰতিটো সংখ্যাৰ বৰ্গমূল (√) লওক আৰু ২-এ ভাগ কৰক।

COS Values: √4/2 → √3/2 → √2/2 → √1/2 → √0/2

3. TAN (Tangent / টেন)

TAN = SIN ÷ COS (ছাইনক কছাইনেৰে ভাগ কৰক।)

0 → 1/√3 → 1 → √3 → ∞ (Not Defined / অসংজ্ঞায়িত)

4. COT (Cotangent / ক'টেন)

COT = 1 ÷ TAN (টেনৰ বিপৰীত মান।)

Values: ∞ → √3 → 1 → 1/√3 → 05. SEC (Secant / ছেক)

SEC = 1 ÷ COS (কছাইনৰ বিপৰীত মান।)

Values: 1 → 2/√3 → √2 → 2 → ∞ (Not Defined / অসংজ্ঞায়িত)6. COSEC (Cosecant / ক'ছেক)

COSEC = 1 ÷ SIN (ছাইনৰ বিপৰীত মান।)

Values: ∞ → 2 → √2 → 2/√3 → 1

Golden Rule (সোণালী নিয়ম)