By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
<h3>How to prove this point lies on the unit circle?</h3>
In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
Read more on unit circle here: brainly.com/question/9797740
#SPJ1
Answer:
6283.2
Step-by-step explanation:
=
=6283.18531
=6283.2(correct to the tenths place)
Answer: The mechanic who worked 5 hours charged $45 per hour while the mechanic who worked for 15 hours charged $105 per hour.
Step-by-step explanation:
Let x be the rate of mechanic who worked 5 hours
And y, the rate of mechanic who worked 15 hours
Represent the question in an equation
x + y = 150.............. equation 1
5x + 15y = 1800........equation 2
x + y = 150, x = 150 -y
Substitute the value of x into equation 2 to get y
= 5 (150 -y) + 15y = 1800
Then open the bracket
750 - 5y + 15y = 1800
750 + 10y = 1800
10y = 1800 - 750
10y= 1050 (divide both sides by 10)
y = 1050/10
y = 105
Substitute the value of y into equation 1 to get the value of x
x + 105 = 150
x = 150 - 105
x = 45
Therefore, the mechanic who worked 5 hours charged $45 per hour while the mechanic who worked for 15 hours charged $105 per hour.
I hope this is clear, mark as brainliest please
Answer:
Step-by-step explanation:
