Answer:
Step-by-step explanation:
given the expression;
cos(2x) = cos(x)
According to trig identity;
cos(2x) = cos(x+x)
cos(2x) = cos x cos x - sinx sinx
cos(2x) = cos²(x)-sin²(x)
cos(2x) = cos²(x)-(1-cos²x)
cos(2x) = cos²(x)+cos²x-1
cos(2x) = 2cos²(x)-1
2cos²(x)-1 = cos(x)
let P = cosx
2P²-1 = P
2P²-P-1 = 0
Factorize;
2P²-2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P - 1 = 0 and P-1 = 0
P = 1/2 and 1
cosx = 1/2 and cos x = 1
x = arccos 1/2
x = π/3
Also;
x = arccos1
x = 0
Hence the value of x are 0 and π/3
Also the angle = π+ π/3 = 4π/3
The angles are 0, π/3 and 4π/3
Answer:
236.715 ft²
Step-by-step explanation:
The figure consists of the rectangle with sides 15 ft and 4 ft and two semicircles with diameter 15 ft (radius 7.5 ft).
The area of the rectangle is
A₁=15·4=60 ft²
The area of two semicircles together is the area of circle. Thus,
A₂=πr²=π·7.5²=56.25π≈176.715 ft²
The area of the figure is
A=A₁+A₂=60+176.715=236.715 ft²
Answer:
Center of dilation origin, The scale factor is 4, The dilation mapping is (x, y) → (4x,4y) and The image represents the shape of the triangle.
Step-by-step explanation:
Given Hector is making an art project by cutting and gluing fabric shapes to a wooden board. His design includes two similar triangles, with one 4 times the size of the other. He cuts the smaller fabric triangle and traces it onto grid paper. we have to tell how he can use the tracing to make a pattern for the larger fabric triangle.
Apply the center of dilation origin.
The scale factor is 4
The dilation mapping is (x, y) → (4x,4y)
The image represents the shape of the triangle.
Answer:
Answer 44
Step-by-step explanation:
I'll do some of it. You can supply some of the vocabulary.
<Q = 56 degrees The triangle is isosceles.
<PRQ = 180 - 56 - 56 All triangles have 180 degrees.
<PRQ = 68 Do the subtraction
<PRQ = <SRT Why is this so? You have the term.
<TRS = 68 degrees The reason is the same as the last part.
<T = <RST The triangle is isosceles (2 equal angles)
<T = 68 Two equal angles = the same degrees
S = 180 - <T - < RST S is the left over from the 2 equal angles.
S = 180 - 68 + 68 Substitute.
S = 44
8 x 3 = 24
24 + 3 = 27
27/8 is equivalent
