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Question bank: Trigonometry: Product-to-Sum Transformation

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Question 1:

Medium

In a Physics competition, students need to solve a problem involving electromagnetic waves. One of the challenges involves applying the product-to-sum transformation, using the Prostaférese formulas. Given the product of sines and cosines in the expression A*sin(3x)*cos(4x), perform the following steps: (a) Apply the Prostaférese formula to transform the product into a sum, replacing Asin(3x)cos(4x) with an expression involving only sums and subtractions of sines and cosines. (b) Describe a possible practical application of the product-to-sum transformation technique in this specific context of the Physics competition.

Trigonometry: Product-to-Sum Transformation

Question 2:

Medium

Trigonometry: Product-to-Sum Transformation

Question 3:

Medium

Trigonometry: Product-to-Sum Transformation

Question 4:

Very Easy

An observer is located 100 meters from the base of a building. He sees the top of the building forming an angle of elevation of 30 degrees with the ground. Using trigonometric relationships and the Prosthaphaeresis Formulas, determine the height of the building, considering the sine of 30 degrees equal to 0.5 and the cosine of 30 degrees equal to √3/2.

Trigonometry: Product-to-Sum Transformation

Multidisciplinary Question

Question 5:

Medium

Trigonometry: Product-to-Sum Transformation

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