Trigonometric Functions and Identities

The video tutorial explains how to determine the exact trigonometric function value of sine 105 degrees using the sum and difference identity. It begins by identifying angles with known function values that can be added or subtracted to equal 105 degrees, such as 60 and 45 degrees. The tutorial then applies the sum identity to calculate the sine of 105 degrees, using reference triangles to find exact trigonometric values. The process is concluded with the final result, emphasizing the importance of using known angles and identities for precise calculations.

What is the main goal of the video tutorial?

• To memorize trigonometric tables.

• To understand the history of trigonometry.

• To determine the exact trigonometric function value of sine 105 degrees using identities.

• To learn how to calculate sine 105 degrees using a calculator.

Which angles are typically used to find exact trigonometric values?

• Angles like 25, 55, 85, and 115 degrees.

• Angles like 10, 20, 50, and 80 degrees.

• Angles like 30, 60, 45, and 90 degrees.

• Angles like 15, 75, 105, and 135 degrees.

What is one combination of angles that sum to 105 degrees?

• 30 degrees + 75 degrees

• 60 degrees + 45 degrees

• 90 degrees + 15 degrees

• 45 degrees + 60 degrees

Which identity is used to find the sine of a sum of two angles?

• Sine of a product identity

• Cosine of a sum identity

• Tangent of a sum identity

• Sine of a sum identity

What is the sine of 60 degrees?

• 1/2

• Square root 3 over 2

• Square root 2 over 2

• 1

What is the cosine of 45 degrees?

• 1

• Square root 2 over 2

• Square root 3 over 2

• 1/2

What is the result of rationalizing 1 over square root 2?

• Square root 2 over 2

• Square root 3 over 2

• 1/2

• 1

What is the cosine of 60 degrees?

• Square root 3 over 2

• 1/2

• Square root 2 over 2

• 1

What is the final expression for sine 105 degrees?

• Square root 3 over 2 + Square root 2 over 2

• Square root 3 over 4 + Square root 2 over 4

• Square root 6 over 4 + Square root 2 over 4

• Square root 6 over 2 + Square root 2 over 2

Why can't the radicals in the final expression be added?

• They are already simplified.

• They are not like radicals.

• They are in different units.

• They are in different quadrants.