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°.
The word 'Cosine' actually comes from the Latin phrase complementi sinus, which literally translates to 'the sine of the complement'!
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)
Let's apply the rule to 50°:
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.
If you need the exact numerical value for a calculator problem: sin(50°) = cos(40°) ≈ 0.7660
Since sin 50° is exactly equal to cos 40°, dividing them by each other will give the result **1**.
What Comes After Crore? (Indian Numeral System)
Learn what comes after a Crore in the Indian Numeral System. Discover Arab, Kharab, Neel, and how to count zeros in massive numbers up to Maha Shankh.
What Is an Armstrong Number? — Definition, Examples and List
An Armstrong number equals the sum of its digits each raised to the power of the number of digits. Examples: 153, 370, 371, 407 (3-digit); 1634, 8208, 9474 (4-digit).
What is Ascending Order?
Learn the definition of ascending order in mathematics. Understand the difference between ascending (smallest to largest) and descending (largest to smallest) order.
Which of the Following Is Not an Irrational Number?
Irrational numbers cannot be written as p/q (e.g., √2, π, e). √4=2, √9=3 are rational. Full explanation of rational vs irrational numbers with examples and MCQ tips.
Which Value of r Indicates a Stronger Correlation
The value of r closer to ±1 indicates a stronger correlation. r = +1 perfect positive, r = −1 perfect negative, r = 0 no correlation. Statistics Class 11/12.
Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.