Trigonometric Functions and Properties

The video tutorial explores special numbers in right angle triangles, focusing on trigonometric ratios for specific angles: 30, 45, and 60 degrees. It explains why these angles have special values and demonstrates how to calculate sine, cosine, and tangent for these angles using complementary relationships and Pythagorean theorem. The tutorial emphasizes understanding these concepts without relying solely on calculators, highlighting the importance of exact values in trigonometry.

What is the significance of special numbers in right-angle triangles?

• They always form equilateral triangles.

• They result in whole number side lengths.

• They are used to calculate area.

• They are only applicable to isosceles triangles.

What is the sine value of a 30-degree angle?

• 1.0

• 0.75

• 0.5

• 0.25

How do you calculate the third side of a right-angle triangle if two sides are known?

• Using the tangent rule

• Using Pythagoras' theorem

• Using the cosine rule

• Using the sine rule

What is the cosine of a 30-degree angle?

• √3/2

• 1/√3

• 1/2

• √2/2

Why are 30 and 60 degrees considered complementary angles?

• Their sum is 90 degrees.

• They are both acute angles.

• They have the same sine value.

• They form an equilateral triangle.

What is the tangent of a 60-degree angle?

• 0

• 1

• 1/√3

• √3

What is unique about the 45-degree angle in a right-angle triangle?

• It is its own complement.

• It forms an equilateral triangle.

• It has a sine value of 1.

• It is always the largest angle.

What is the sine value of a 45-degree angle?

• 1/2

• √3/2

• √2/2

• 1

What is the tangent of a 45-degree angle?

• √3

• √2

• 1

• 0

How many exact trigonometric values were introduced in the lesson?

• 9

• 3

• 6

• 12