Trigonometry Concepts and Applications

The video tutorial covers trigonometric ratios, expanding from right-angled triangles to any angle using the unit circle. It introduces the sine and cosine rules for non-right-angled triangles and explains how to find the area of any triangle using trigonometry. The tutorial also derives the area formula using sine and algebra, and discusses the cosine rule and the concept of the included angle.

Which trigonometric ratio is defined as the opposite side over the hypotenuse in a right-angled triangle?

• Sine

• Cosine

• Tangent

• Secant

What is the purpose of introducing the unit circle in trigonometry?

• To limit angles to acute angles

• To simplify the calculation of hypotenuse

• To allow for any angle measurement

• To restrict calculations to right-angled triangles

What do the sine and cosine rules allow you to calculate?

• Only right-angled triangles

• Only equilateral triangles

• Any triangle, regardless of angles

• Only isosceles triangles

What is the formula for the area of a triangle when the perpendicular height is not available?

• Base times height

• a squared plus b squared

• Half base times height

• Half a b sine C

What is the special name given to the perpendicular height in a triangle?

• Hypotenuse

• Altitude

• Median

• Base

In the cosine rule, what is the significance of the included angle?

• It is any angle in the triangle

• It is the angle between the two known sides

• It is the smallest angle in the triangle

• It is the angle opposite the longest side

What does the cosine rule start with?

• d squared

• c squared

• b squared

• a squared

Which angle is used in the area of a triangle formula involving sine?

• Any angle

• The smallest angle

• The included angle

• The largest angle

What is the relationship between the sides and angles in the cosine rule?

• The angle is opposite the longest side

• The angle is between the two known sides

• The angle is the smallest in the triangle

• The angle is opposite the shortest side

What is the purpose of using algebra in finding the height in a triangle?

• To find the longest side

• To express height in terms of other known values

• To eliminate the need for a calculator

• To simplify the base