12
QuizMultiple Choice

Trigonometric Functions — Test

Question 12 • Mathematics III

Which transformations are needed to change the parent cosine function to y is equal to 0 point 3 5 cosine open paren 8 times open paren x minus pi over 4 close paren close paren ?

Answer
A
vertical stretch of 0 point 3 5 , horizontal stretch to a period of 16 pi , phase shift of pi over 4 units to the right
B
vertical stretch of 0 point 3 5 , horizontal stretch to a period of pi over 4 , phase shift of pi over 4 units to the right
C
vertical compression of 0 point 3 5 , horizontal compression to a period of 4 pi , phase shift of pi over 4 units to the left
D
vertical compression of 0 point 3 5 , horizontal compression to a period of pi over 4 , phase shift of pi over 4 units to the right

Explanation

The coefficient 0.35 outside the cosine makes a vertical compression by a factor of 0.35. The 8 multiplying the parentheses changes the period from 2π to 2π ÷ 8 = π/4, which is a horizontal compression. Since the expression is x − π/4, the graph shifts π/4 units to the right. These transformations match choice B.

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