You're given that φ is an angle that terminates in the third quadrant (III). This means that both cos(φ) and sin(φ), and thus sec(φ) and csc(φ), are negative.
Recall the Pythagorean identity,
cos²(φ) + sin²(φ) = 1
Multiply the equation uniformly by 1/cos²(φ),
cos²(φ)/cos²(φ) + sin²(φ)/cos²(φ) = 1/cos²(φ)
1 + tan²(φ) = sec²(φ)
Solve for sec(φ) :
sec(φ) = - √(1 + tan²(φ))
Given that cot(φ) = 1/4, we have tan(φ) = 1/cot(φ) = 1/(1/4) = 4. Then
sec(φ) = - √(1 + 4²) = -√17
Answer:
The width is 11 units.
Step-by-step explanation:
First, you have to add 4 to 18 which is 22. Then divide by 2.
The exact calculations:
Principal, P=3000
interest rate = 33% per year
Period, t=10 years
Future value
Interest
= future value - principal
= 81337.92-3000
=
78337.92 (to the nearest cent)
The square root of 142 is 11.916
Answer:
60ft
Step-by-step explanation:
I have not done this kind of work in a while but if you scale each side of the square by 6 is should increase to a perimeter of 60ft