Exams › SSC CGL (Prelims) › General

If cos B = p/q where B lies in the interval (0, pi/2), express sin B in terms of p and q.

1. sqrt(q^2 - p^2) / q
2. sqrt(q^2 + p^2) / p
3. sqrt(q^2 - p^2) / p
4. p / sqrt(q^2 - p^2)

Correct answer: sqrt(q^2 - p^2) / q

Solution

From sin^2 B = 1 - cos^2 B = 1 - (p/q)^2 = (q^2 - p^2)/q^2, taking the positive root (first quadrant) gives sin B = sqrt(q^2 - p^2)/q.

Related SSC CGL (Prelims) General questions

• A shopkeeper sells rice at a discount of 6% on the marked price but uses a weight that is 25% less than the actual weight. Find his overall profit percentage.
• The profit made on an article sold for ₹2400 is equal to the loss incurred when it is sold for ₹2000. What will be the profit or loss percentage if the article is sold for ₹2200?
• Train A leaves Station X at 5:00 AM at 50 km/h. Train B leaves Station Y at 7:30 AM at 80 km/h. Both trains move towards each other. The distance between the stations is 500 km. When do they meet?
• A wholesaler marks up goods by 50% and gives a 12% trade discount. A retailer marks up by 20% and offers an 8% discount. The customer pays ₹12,216. What is the wholesaler's cost price approximately?
• If A : B = 3 : 4, B : C = 5 : 6, and C : D = 7 : 8, then find B : D.
• What is the result of $3^2 + 5 \div 0.8$?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →