Complementary Angles in Trigonometry

The video tutorial explains how to solve a trigonometry problem involving complementary angles. It begins by introducing the concept of complementary angles and how they relate to sine and cosine. The instructor demonstrates how to find the cosine of beta using given information and complementary relationships. A right-angled triangle is constructed to visualize the trigonometric ratios, and Pythagoras' theorem is used to calculate the cosine of alpha. The tutorial emphasizes understanding the relationships between angles and sides in a triangle.

What is the relationship between complementary angles in trigonometry?

• They add up to 180 degrees.

• They add up to 90 degrees.

• They are equal.

• They are supplementary.

If sin(alpha) = 5/13, what is cos(beta) when alpha and beta are complementary?

• 13/5

• 1

• 12/13

• 5/13

How can you represent complementary angles in a right-angled triangle?

• As two angles that are supplementary.

• As two angles that add up to 180 degrees.

• As two angles that add up to 90 degrees.

• As two angles that are equal.

In a right-angled triangle, if sin(alpha) = 5/13, which side is opposite to alpha?

• The opposite side

• The adjacent side

• The hypotenuse

• The base

What is the hypotenuse of a triangle if sin(alpha) = 5/13?

• 5

• 13

• 12

• 1

How do you find the adjacent side in a right-angled triangle using Pythagoras' theorem?

• By adding the squares of the other two sides.

• By subtracting the square of the opposite side from the hypotenuse squared.

• By dividing the hypotenuse by the opposite side.

• By multiplying the opposite side by the hypotenuse.

What is the value of cos(alpha) if the adjacent side is 12 and the hypotenuse is 13?

• 1

• 13/12

• 12/13

• 5/13

If sin(alpha) = 5/13, what is sin(beta) when alpha and beta are complementary?

• 1

• 13/5

• 12/13

• 5/13

What is the significance of complementary angles in trigonometry?

• They allow the use of sine and cosine interchangeably.

• They are used to calculate the area of a triangle.

• They are used to find the perimeter of a triangle.

• They help in finding the sum of angles in a triangle.

Why is it important to understand the concept of complementary angles?

• To understand the properties of parallel lines.

• To calculate the volume of a cylinder.

• To solve algebraic equations.

• To apply trigonometric identities effectively.