Evaluating the half angle for cosine 15 degrees

The video tutorial explains how to evaluate angles using sum, difference, and half-angle formulas, focusing on the example of 15 degrees. It highlights the common mistakes students make, such as incorrectly substituting angles in the half-angle formula. The tutorial also covers techniques for simplifying fractions in trigonometric calculations, providing a step-by-step approach to solving these problems. The final section concludes with the correct calculation and interpretation of the results.

What is the purpose of using the sum and difference formulas in trigonometry?

• To solve quadratic equations.

• To simplify complex numbers.

• To convert angles from degrees to radians.

• To find the exact value of angles not directly available in trigonometric tables.

When using the half-angle formula for cosine, what is the correct approach to find the cosine of 15 degrees?

• Subtract 15 degrees from 45 degrees.

• Double the angle to 30 degrees and use it in the formula.

• Use 15 degrees directly in the formula.

• Add 15 degrees to 45 degrees.

What is the biggest mistake students make when using the half-angle formula?

• Not simplifying the expression.

• Using the angle directly without doubling it.

• Forgetting to divide by two.

• Using the wrong trigonometric function.

How can you simplify the expression 1 + sqrt(3)/2 divided by 2?

• Multiply both the numerator and denominator by 2.

• Add 2 to both the numerator and denominator.

• Subtract 1 from the numerator.

• Divide the numerator by 4.

What is the final simplified form of the expression obtained from the half-angle formula for cosine of 15 degrees?

• ± sqrt(3 - sqrt(2))/2

• ± sqrt(2 - sqrt(3))/2

• ± sqrt(3 + sqrt(2))/2

• ± sqrt(2 + sqrt(3))/2