Trigonometric Functions and Angles

This video tutorial covers the basics of trigonometric ratios: sine, cosine, and tangent. It explains how to use these ratios to find missing angles in right-angled triangles when given two sides. The tutorial includes several example problems and practice exercises to reinforce the concepts. The video concludes with a summary and additional practice questions for viewers to try on their own.

What is the primary purpose of trigonometric ratios in right-angled triangles?

• To find the area of the triangle

• To find the missing angles and lengths

• To determine the type of triangle

• To calculate the perimeter

Which side of a right-angled triangle is always the longest?

• Adjacent

• Opposite

• Base

• Hypotenuse

What does the 'opposite' side refer to in a right-angled triangle?

• The longest side

• The side next to the angle

• The side opposite the right angle

• The side opposite the angle in question

Which trigonometric ratio is represented by 'sin'?

• Hypotenuse over Opposite

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

• Opposite over Adjacent

What is the formula for cosine in a right-angled triangle?

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

• Opposite over Adjacent

• Hypotenuse over Adjacent

In the tangent ratio, which sides are compared?

• Hypotenuse and Adjacent

• Opposite and Adjacent

• Opposite and Hypotenuse

• Adjacent and Hypotenuse

If cos(x) = 8/10, what is the angle x to one decimal place?

• 60.0 degrees

• 53.1 degrees

• 45.0 degrees

• 36.9 degrees

Which function is used to find an angle from its cosine value?

• Inverse Cosine

• Inverse Sine

• Inverse Secant

• Inverse Tangent

If cos(x) = 5/9, what is the angle x to one decimal place?

• 56.3 degrees

• 45.0 degrees

• 30.0 degrees

• 60.0 degrees

What is the inverse function used to find an angle from its tangent value?

• Inverse Sine

• Inverse Cosine

• Inverse Tangent

• Inverse Secant