What angle does the tangent to the curve y (x) = sin^2 (x/4) + 12sin (x/4) at x=4_ make with the x-axis?

Express your answer to 3 significant figures. Choose the smaller angle, i. e., your answer should be positive and less than 90 degrees.

Question

Nylah Duarte

Mathematics

5 September, 01:32

What angle does the tangent to the curve y (x) = sin^2 (x/4) + 12sin (x/4) at x=4_ make with the x-axis?

Express your answer to 3 significant figures. Choose the smaller angle, i. e., your answer should be positive and less than 90 degrees.

+4

Answers (1)

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Brenton · Answer 1

y (x) = sin^2 (x/4) + 12sin (x/4)

y (x) = sin^2 (x/7) + 16sin (x/7)

From the Chain Rule,

y' (x) = 2sin (x/4) * (1/4) cos (x/4) + 12 (1/4) cos (x/4).

At x=4pi, the slope of the tangent line is

y' (4pi) = 2sin (4pi/4) * (1/4) cos (4pi/4) + 12 (1/4) cos (4pi/4).

= 2sin (pi) * (1/4) cos (pi) + 12 (1/4) cos (pi)

= 2 (0) (1/4) (-1) + 12 (1/4) (-1)

= - 3

The angle (in radians) that the tangent line makes to the positive x-axis is

pi - arctan (3) = 1.249 rad = 71.565 degree

What angle does the tangent to the curve y (x) = sin^2 (x/4) + 12sin (x/4) at x=4_ make with the x-axis?Express your answer to 3 significant figures. Choose the smaller angle, i. e., your answer should be positive and less than 90 degrees.

What angle does the tangent to the curve y (x) = sin^2 (x/4) + 12sin (x/4) at x=4_ make with the x-axis?

Express your answer to 3 significant figures. Choose the smaller angle, i. e., your answer should be positive and less than 90 degrees.