Study Guides/Maths/Value of cot 30
Study Guide · Maths

What is the Value of cot(30°)?

In Class 10 Trigonometry, memorizing the values of sine, cosine, and tangent for standard angles is mandatory. However, you don't need to memorize the values for cotangent (cot) if you know the basic formulas.

Question (Click to Flip)

What is the value of cot(90°)?

Answer

We know cot(90) = cos(90) / sin(90). Since cos(90) is 0 and sin(90) is 1, the answer is 0/1 = 0.

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Key Facts

Due to the complementary angles theorem, the value of cot(30°) is exactly the same as the value of tan(60°), which is also √3.

The Exact Value

The exact value of cot(30°) is √3 (Root 3).

(In decimal form, √3 is approximately 1.732).

Derivation Method 1: The Reciprocal of Tan

The easiest way to find cotangent is to remember that cot(θ) is the mathematical reciprocal (inverse) of tan(θ).

Formula: cot(θ) = 1 / tan(θ)

  1. From the standard trig table, we know that tan(30°) = 1 / √3.
  2. Therefore, cot(30°) = 1 / (1 / √3)
  3. When you flip the fraction, the √3 goes to the top.
  4. Result = √3.

Derivation Method 2: Cosine divided by Sine

If you only remember the sine and cosine tables, you can use the ratio formula:

Formula: cot(θ) = cos(θ) / sin(θ)

  1. From the table: cos(30°) = √3 / 2
  2. From the table: sin(30°) = 1 / 2
  3. Divide them: cot(30°) = (√3 / 2) ÷ (1 / 2)
  4. The 2s in the denominators cancel each other out.
  5. Result = √3.

Questions and Answers

What is the value of cot(90°)?+

We know cot(90) = cos(90) / sin(90). Since cos(90) is 0 and sin(90) is 1, the answer is 0/1 = **0**.

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