$sin (2 \alpha) =2\cdot sin \alpha \cdot cos \alpha \\cos(2 \alpha )=1-2sin^2 \alpha \\-------------------- \\cos2x-sin2x=1-2sin2x\\cos2x+sin2x=1\\1-2sin^2x+2sinx\cdot cosx=1\\-2sinx(sin x-cosx)=0\\ -2sinx=0\ \ \ \ or\ \ \ \ sinx-cosx=0\\\\1)\ -2sinx=0\ \ \Leftrightarrow\ \ sinx=0\ \ \Leftrightarrow\ \ x_1=k \pi \ \ and\ \ k\in I\\2)\ \ sinx-cosx=0\ \ \Leftrightarrow\ \ sinx=cosx\ /:cosx\ \ \ \ \ \wedge\ \ \ \ cos x \neq 0\\tanx=1\ \ \Leftrightarrow\ \ x_2= \frac{ \pi }{4} +k \pi \ \ and\ \ k\in I$

3 0

3 years ago

Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left

Liono4ka [1.6K]

All the transformation performed on a pentagon does not affect on its size or its length
It is not stretched or shrunk
So,
The original and transformed images are congruent

8 0

3 years ago

What is the length of the hypotenuse of a right triangle with legs that are 7 and 8 inches

Mrrafil [7]

B). 10.63
Because 7^2=49 and 8^2=64 then 49+64=113 then the square root of 113 is 10.63

5 0

3 years ago

Read 2 more answers

Given f(x)=5-3x, if f(x)=-19, find x

Dafna1 [17]

X would equal 8

Step-by-step explanation:

5-3(8) = -19

5 multiplied by negative 3 times 8 equals negative 19

negative 3 times 8 equals negative 24 plus 5 equals 19

7 0

3 years ago