You can determine if a number is rational if it can be represented as a terminating or repeated decimal, but if it can not, then the number is irrational.
Answer:
1. 0, 2 π , π , 2 π/3 , 4 π/3
2. 7 π/6 , 11 π/6
Step-by-step explanation:
1. we want to find the value of theta
Let us represent theta by x for ease of documentation
So we have ;
sin 2x + sin x = 0
Mathematically;
sin 2x = 2sinxcosx
So;
2 sin x cos x + sin x = 0
sin x (2 cos x + 1) = 0
sin x = 0
or
2cos x + 1 = 0
x = arc sin (0)
within the given range;
x = theta = 0 , 2 π , π
For;
2 cos x + 1 = 0
2cos x = -1
cos x = -1/2
cos x = -0.5
x = arc cos (-0.5)
x = 2 π/3 , 4 π/3
2. cos 2 x = 1 + sin x
Mathematically;
cos 2 x = 1-2 sin^2x
let sin x = y
1-2y^2 = 1 + y
y = -2y^2
1 = -2y
y = -1/2
y = -0.5
sin x = y
sin x = -0.5
x = arc sin (-0.5)
x = 7 π/6 , 11 π/6
Answer:
Angle 5 = 35 degrees
Step-by-step explanation:
A straight line is equal to 180 degrees, meaning 1 + 2 + 5 = 180 degrees because they make up a straight line.
Angle 2 = 55 degrees
Angle 1 = 90 degrees (because it is a right angle)
Angle 5 = ?
Set up an equation:
90 + 55 + angle 5 = 180
145 + angle 5 = 180
Angle 5 = 35
Answer:
u = 12
Step-by-step explanation:
The equation is showing 5(u) = 60
<u>Begin: 5(u)= 60</u>
2. Divide the 5 from both sides to get the u-value alone.
a) 5u/5 = u b) 60/5 = 12
<u>Now: u = 12</u>
