Understanding Sine of Seven Pi Over 12

The video tutorial explains how to find the sine of 7π/12 without using a calculator. It begins by visualizing the angle on the unit circle and understanding the sine as the y-coordinate. The tutorial then explores using trigonometric identities and special right triangles, such as 30-60-90 and 45-45-90, to decompose the angle into known values. Finally, the angle addition formula is applied to calculate the sine of 7π/12, resulting in the expression (√2 + √6)/4.

What is the main goal of the video tutorial?

• To visualize the unit circle

• To calculate the sine of seven pi over 12 using a calculator

• To explain the concept of radians

• To find the sine of seven pi over 12 without a calculator

What does the sine of an angle represent on the unit circle?

• The x-coordinate of the point

• The angle in degrees

• The radius of the circle

• The y-coordinate of the point

Which trigonometric function is used to relate the sides of the triangle in the unit circle?

• Tangent

• Sine

• Cosine

• Secant

What type of triangles are used to decompose the angle seven pi over 12?

• Scalene triangles

• 30-60-90 and 45-45-90 triangles

• Right triangles with unknown angles

• Equilateral triangles

What is the angle addition formula used for in this context?

• To find the hypotenuse of a triangle

• To convert radians to degrees

• To express the sine of a sum of angles

• To calculate the area of a triangle

What is the sine of pi over four?

• 1/2

• 1

• Square root of 2 over 2

• Square root of 3 over 2

What is the cosine of pi over three?

• Square root of 2 over 2

• 1

• 1/2

• Square root of 3 over 2

What is the final expression for sine of seven pi over 12?

• Square root of 2 over 2

• Square root of 3 over 2

• 1

• Square root of 2 plus square root of 6, all over 4

Which trigonometric identity is used to find the sine of seven pi over 12?

• Pythagorean identity

• Angle addition formula

• Double angle formula

• Half angle formula

What is the cosine of pi over four?

• 1/2

• Square root of 2 over 2

• 1

• Square root of 3 over 2