5
If tan θ = —— , calculate the value of cos θ:
4
Recall the definition of the tangent function:
sin θ
tan θ = ————
cos θ
5 sin θ
—— = ————
4 cos θ
Cross multiply:
5 · cos θ = 4 · sin θ
Square both sides:
(5 · cos θ)² = (4 · sin θ)²
5² · cos² θ = 4² · sin² θ
25 · cos² θ = 16 · sin² θ
But sin² θ = 1 – cos² θ. Substitute that for sin² θ into the equation above, then you get
25 · cos² θ = 16 · (1 – cos² θ)
25 · cos² θ = 16 – 16 · cos² θ
Isolate cos² θ:
25 · cos² θ + 16 · cos² θ = 16
(25 + 16) · cos² θ = 16
41 · cos² θ = 16
16
cos² θ = ———
41
4²
cos² θ = ————
(√41)²
Take square root of both sides:
4
cos θ = ± ———
√41
4 4
cos θ = – ——— or cos θ = ——— ✔
√41 √41
The sign of cos θ depends on which quadrant θ lies. Since you first have a positive value for tan θ, then that means θ lies either in the 1st or the 3rd quadrant.
• If θ is a 1st quadrant angle, then
cos θ > 0
4
cos θ = ——— ✔
√41
• If θ is a 3rd quadrant angle, then
cos θ < 0
4
cos θ = – ——— ✔
√41
I hope this helps. =)
Answer:
20
Step-by-step explanation:
You need to create two equations for each company and then set them equal to each other. The keywords base fee means you will pay this amount regardless, so this amount stays constant and it will be the constant in the equation. The other keyword is per. Per will link the variable with the coefficient.
The first equation for company M:
y = 12x + 60
The second equation for company N:
y = 9x + 120
Set the equations equal to each other.
9x + 120 = 12x + 60
Solve for x. I am going to subtract 9x from both sides first.
9x - 9x + 120 = 12x -9x +60
120 = 3x +60
Now, I will subtract 60 from both sides.
120 - 60 = 3x + 60 - 60
60 = 3x
Finally, I will divide both sides by 3
60/3 = 3x/3
x = 20
20 is how many guests it will take for the total cost to be the same.
Answer:
no
Step-by-step explanation:
The second one is the only equivalent equation. Simply plug in each variable in each equation. And compare!
