Let f (x) = 4cosx. Sin (x + pi / 6) find the minimum positive period of F (x)

Let f (x) = 4cosx. Sin (x + pi / 6) find the minimum positive period of F (x)

F (x) = 4cosx times sin (x + divisor 6)
=4[sin(2x+π/6)/2-sin(-π/6)/2]
=4sin(x+π/12)+4sin(π/12)
ω=1,
From the periodic formula
T=2π/ω
=2π.
The minimum positive period of the function f (x) = 4cosx times sin (x + divisor 6) is 2 π
.

Is f (x) = 1 + sin a periodic function

Is... F (x + 2) = 1 + sin faction (x + 2) = 1 + sin faction x * Cos2 faction + sin2 faction * cos faction x = 1 + sin faction x = f (x)

The function f (x) = sin (x / 2-pie / 4), X belongs to R, and the minimum positive period is?

T = 2pai / (1 / 2) = 4pai
T = 2pai / W
(W is the coefficient of x)

The minimum positive period of function f (x) = sin (PIE X / 2) sin (pie (x-1) / 2)

A:
f(x)=sin(πx/2sin[π(x-1)/2]
=sin(πx/2)sin(πx/2-π/2)
=sin(πx/2)cos(πx/2)
=(1/2)sin(πx)
So: the minimum positive period of F (x) t = 2 π / π = 2

As shown in the figure, the chord AC of circle O is 2, the circumference angle ABC is 45 ° and the shadow area is calculated
Here's another problem: as shown in the figure, a square is 4cm in length. After subtracting the four corners, it becomes a regular octagon. Find out the side length and area of the octagon,

Give me a picture

In a right triangle, if there is an acute angle of 30 degrees and the sum of the center line on the hypotenuse and the smaller right side is 18 cm, the length of the hypotenuse is calculated

Small right angle side = hypotenuse × sin30 = 0.5 hypotenuse. If "median line on hypotenuse" refers to the line connecting the middle point of hypotenuse and the vertex of the opposite right angle, since the short right angle side = half of hypotenuse, and the angle between the short right angle side and hypotenuse is 60 degrees, the short right angle side, half of hypotenuse and the median line of hypotenuse form a small regular triangle, so "median line length = half of hypotenuse = short right angle side", Then it is "0.5 bevel + 0.5 bevel = 18cm", "bevel = 18cm"

5. In a right triangle, if there is an acute angle of 30 ° and the difference between the hypotenuse and the smaller right side is 18cm, then the length of the hypotenuse is

36cm
According to the trigonometric function, the right side of 30 degrees in a right triangle is half of the hypotenuse, and then the equation is formulated, 2x-x = 18, x = 18, hypotenuse = 2x = 36cm

Given that the three angles of a right triangle are 90 60 30, can we calculate the length of its three sides

No
Similar triangles look the same
Hope to help you

Write the inverse proposition of "if a triangle is a right triangle, then the acute angle between the bisectors of its two acute angles is 45 degrees", and prove that this proposition is true

The inverse proposition is: if the acute angle between the bisectors of the two angles of a triangle is 45 degrees, then the triangle is a right triangle. It is known that, as shown in the figure, △ ABC, be is the bisector of ∠ ABC, intersecting AC at e, ad is the bisector of ∠ cab, intersecting BC at D, be and ad at O, and ∠ EOA = 45 degrees Ad is the angular bisector of ∠ cab, ∠ OAB = 12 ∠ cab, ∠ oba = 12 ∠ CBA, ∠ OAB + ∠ oba = 12 (∠ cab + ∠ CBA), 〈 180 ° - ∠ AOB = 12 (180 ° - C), 〈 AOB = 90 °+ 12 ∠ C and ∵ - EOA = 45 °, and ∵ - AOB = 135 ° = 90 °+ 12 ∠ C, ∵ - C = 90 °, and ∵ △ ABC are right triangle

What is the acute angle between the bisectors of the two acute angles of a right triangle

If the sum of the angles obtained by bisectors of two acute angles is equal to 45 degrees, then the included angle should be 180-45 = 135 degrees