cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>)
So if both cot(<em>θ</em>) and cos(<em>θ</em>) are negative, that means sin(<em>θ</em>) must be positive.
Recall that
cot²(<em>θ</em>) + 1 = csc²(<em>θ</em>) = 1/sin²(<em>θ</em>)
so that
sin²(<em>θ</em>) = 1/(cot²(<em>θ</em>) + 1)
sin(<em>θ</em>) = 1 / √(cot²(<em>θ</em>) + 1)
Plug in cot(<em>θ</em>) = -2 and solve for sin(<em>θ</em>) :
sin(<em>θ</em>) = 1 / √((-2)² + 1)
sin(<em>θ</em>) = 1/√(5)
Answer:
x = 8
Step-by-step explanation:
Step 1 : Simplify the equation
3(x-5) + 7x = 65
3x - 15 + 7x = 65
Step 2 : Make x the subject
3x + 7x = 65 + 15
10x = 80
x = 80/10
x = 8
!!
36.00 will be enough to pay for fuel because if you multiply the 8.8 gallons of diesel needed by the fuel cost per gallon you get 35.112
