Trigonometry: Understanding Cosine Ratios

This video tutorial continues the trigonometry series by focusing on cosine ratios in right-angled triangles. It explains how to identify the adjacent side and hypotenuse, and how to apply the cosine ratio to calculate unknown sides and angles. The tutorial includes examples of using cosine in right-angled triangles and extends the concept to non-right triangles by creating right triangles. The video emphasizes the importance of understanding the basics of trigonometry to creatively solve complex problems.

What is the cosine of an angle in a right-angled triangle defined as?

• Hypotenuse divided by adjacent side

• Adjacent side divided by opposite side

• Adjacent side divided by hypotenuse

• Opposite side divided by hypotenuse

In a right-angled triangle, which side is always opposite the 90-degree angle?

• Opposite side

• Adjacent side

• Hypotenuse

• Base

If the hypotenuse of a right-angled triangle is 10 cm and the angle is 32 degrees, what is the length of the adjacent side?

• 6.32 cm

• 8.48 cm

• 9.52 cm

• 7.14 cm

What operation is performed when moving a division from one side of an equation to the other in algebra?

• Addition

• Subtraction

• Multiplication

• Division

How do you find an unknown angle using the cosine ratio in a right-angled triangle?

• Use the Pythagorean theorem

• Use the inverse cosine function

• Use the sine ratio

• Use the tangent ratio

What is the inverse cosine of 9/12 approximately equal to?

• 60.8 degrees

• 50.6 degrees

• 41.4 degrees

• 30.2 degrees

How can you apply trigonometric ratios to a non-right-angled triangle?

• By splitting it into right-angled triangles

• By using the cosine rule

• By using the sine rule

• By using the tangent rule

In an isosceles triangle, if one angle is 72 degrees, what is the measure of each angle when split into two right-angled triangles?

• 36 degrees

• 54 degrees

• 60 degrees

• 45 degrees

What is the length of side X if Y is calculated as 2.472135 cm in an isosceles triangle?

• 6.24 cm

• 5.12 cm

• 4.94 cm

• 7.36 cm

How can trigonometric ratios be used creatively in triangle problems?

• To find the number of sides

• To calculate the perimeter

• To determine the type of triangle

• To find the area by determining the height