Exploring Trigonometric Ratios in Depth

This video tutorial introduces trigonometry, focusing on trig ratios like sine and tangent. It explains how these ratios are derived from similar triangles and provides a mnemonic, SOHCAHTOA, to help remember them. The tutorial includes examples and emphasizes the importance of simplifying fractions in trigonometric calculations.

What is the significance of the 45-45-90 triangle in trigonometry?

• Its angles sum up to 180 degrees

• It is the only type of right triangle

• Its side ratios remain consistent regardless of size

• It has no significance

What is the basis of trigonometry?

• The sum of angles in a triangle

• The proportional sides of similar triangles

• The ratios between angles of triangles

• The difference between the sides of triangles

How does trigonometry relate to similar triangles?

• It determines if triangles are similar

• It calculates the area of triangles

• It finds the height of triangles

• It uses the proportional sides of similar triangles

What does the sine of an angle represent?

• Hypotenuse over opposite

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

How do you write the cosine of an angle?

• Opposite over adjacent

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Hypotenuse over opposite

In a right triangle, what does tangent represent?

• Adjacent over opposite

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Opposite over adjacent

What is the mnemonic used to remember trig ratios?

• HOTASACOS

• SOHCAHTOA

• COSAHTOS

• TOAHASOC

What does the Pythagorean theorem help to find in trigonometry?

• The sum of angles

• The length of the hypotenuse

• The ratio of sides

• The difference between angles

What is the purpose of simplifying fractions in trigonometry?

• To find the exact value of angles

• To make calculations easier

• To change the ratio values

• To prove theorems

What is the relationship between the sine of one angle and the cosine of its complementary angle in a right triangle?

• They are inverses

• They are opposites

• They are unrelated

• They are equal