Trigonometric Functions and Angle Verification

Vin demonstrates how to use angle sum formulas to find exact values of trigonometric expressions. He solves two problems: cosine of 105 degrees and sine of 17 pi over 12. For cosine, he uses significant angles to break down 105 degrees into 60 and 45 degrees, applying the cosine angle sum formula. He verifies the result using a calculator. For sine, he initially sets angles but refines the approach by breaking down 5 pi over 12 into 30 and 45 degrees in radians, applying the sine angle sum formula. The results are verified for accuracy.

What is the primary goal of using angle sum formulas in trigonometry?

• To approximate values of trigonometric expressions

• To simplify trigonometric identities

• To convert angles from degrees to radians

• To find the exact values of trigonometric expressions

Which two angles are used in the cosine angle sum formula to find the exact value of cosine 105 degrees?

• 0 and 105 degrees

• 60 and 90 degrees

• 45 and 60 degrees

• 30 and 75 degrees

What is the exact value of cosine 105 degrees using the angle sum formula?

• Square root 6 minus square root 2 all over 4

• Square root 3 minus square root 2 all over 4

• Square root 2 minus square root 6 all over 4

• Square root 2 plus square root 6 all over 4

How can you verify the calculated value of cosine 105 degrees?

• By using a calculator to compare decimal values

• By using a sine table

• By converting to radians

• By using a protractor

What is the initial approach to solve sine of 17 pi over 12?

• Using the sine angle sum formula with angles pi and 5 pi over 12

• Using the cosine angle sum formula with angles pi and 5 pi over 12

• Using the cotangent angle sum formula with angles pi and 5 pi over 12

• Using the tangent angle sum formula with angles pi and 5 pi over 12

What is the degree equivalent of 5 pi over 12?

• 105 degrees

• 60 degrees

• 75 degrees

• 90 degrees

Which angles are used in the final approach to solve sine of 17 pi over 12?

• Pi over 4 and pi over 3

• Pi over 6 and pi over 3

• Pi over 6 and pi over 4

• Pi over 3 and pi over 4

What is the exact value of sine 17 pi over 12 using the angle sum formula?

• Negative square root 6 minus square root 2 all over 4

• Negative square root 6 plus square root 2 all over 4

• Square root 6 plus square root 2 all over 4

• Square root 6 minus square root 2 all over 4

What is the significance of verifying the result of sine 17 pi over 12?

• To ensure the angle is in the correct quadrant

• To confirm the calculation is correct

• To check if the angle is less than 360 degrees

• To verify the angle is in radians

What is the final step in verifying the solution for sine 17 pi over 12?

• Using a calculator to check the decimal value

• Comparing the result with a sine table

• Using a protractor to measure the angle

• Converting the result to degrees