Relationship between sin 50° and cos 40°

In Trigonometry (Class 10 and 11), you don't always need to memorize the exact decimal values of every angle. Understanding the relationship between complementary angles is a powerful shortcut to solve problems involving angles like 50° and 40°.

Question (Click to Flip)

What is the value of (sin 50° / cos 40°)?

Answer

Since sin 50° is exactly equal to cos 40°, dividing them by each other will give the result 1.

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Key Facts

The word 'Cosine' actually comes from the Latin phrase complementi sinus, which literally translates to 'the sine of the complement'!

The Complementary Angle Theorem

Two angles are complementary if they add up to 90°. Here, 50° + 40° = 90°.

In trigonometry, the Sine and Cosine functions are 'co-functions'. The rule states: sin(θ) = cos(90° - θ) cos(θ) = sin(90° - θ)

Proving sin 50° = cos 40°

Let's apply the rule to 50°:

sin(50°) = cos(90° - 50°)
sin(50°) = cos(40°)

Therefore, the value of sin 50° is exactly the same as the value of cos 40°. If a math problem asks you to evaluate sin 50° - cos 40°, the answer is 0.

Exact Decimal Value

If you need the exact numerical value for a calculator problem: sin(50°) = cos(40°) ≈ 0.7660

Questions and Answers

What is the value of (sin 50° / cos 40°)?+

Since sin 50° is exactly equal to cos 40°, dividing them by each other will give the result **1**.

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