Understanding the Algebraic Approach to Finding the Sine of 72 Degrees

What is the initial step in finding the sine of 72 degrees using an algebraic approach?

• Applying the Pythagorean identity

• Setting x equal to 72 degrees

• Using a calculator

• Using the sine addition formula

What is the result of multiplying both sides of the equation by 5?

• 5x equals 45 degrees

• 5x equals 360 degrees

• 5x equals 180 degrees

• 5x equals 90 degrees

Which trigonometric identity is used to expand the sine of 2x?

• Triple angle identity

• Pythagorean identity

• Double angle identity

• Sine addition formula

What happens to the sine of 360 degrees in the equation?

• It becomes one

• It becomes zero

• It doubles

• It remains unchanged

Why is the Pythagorean identity used in the equation?

• To eliminate cosine

• To eliminate sine

• To find the exact value

• To simplify the equation

What substitution is made to simplify the trigonometric equation?

• u equals sine of x

• u equals cotangent of x

• u equals tangent of x

• u equals cosine of x

What form does the equation take after substitution?

• Linear equation

• Exponential equation

• Cubic equation

• Quadratic equation

Which formula is used to solve for u squared?

• Quadratic formula

• Cosine rule

• Binomial theorem

• Sine rule

Why is the negative solution ignored when solving for sine of 72 degrees?

• 72 degrees is in the second quadrant

• Sine is negative in the first quadrant

• Sine is positive in the second quadrant

• 72 degrees is in the first quadrant

What is the exact value of sine 72 degrees as verified by the calculator?

• Square root of 2 divided by 4 times square root of 5 plus square root of 5

• Square root of 2 divided by 3 times square root of 5 plus square root of 5

• Square root of 2 divided by 4 times square root of 3 plus square root of 3

• Square root of 3 divided by 4 times square root of 5 plus square root of 5