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:
2
Step-by-step explanation:
Step 1: Write out equation g(f(a))
1/√a
Step 2: Plug in 0.25 for <em>a</em>
1/√0.25
You answer should be 2
 
        
             
        
        
        
The number of classes Anna can take so the total cost for the month will be the same is 5.
The monthly cost would be  $37.50.
<h3>When would the total cost be the same?</h3>
When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10
In order to determine the value of x, take the following steps:
- Combine similar terms: 7.5x - 5.5x = 10 
- Add similar terms: 2x = 10 
- Divide both sides by 2 : 10 /2 = 5
Monthly cost when the cost is the same: 7.5 x 5 = $37.50
To learn more about cost, please check: brainly.com/question/25711114
#SPJ1
 
        
             
        
        
        
Parallel lines will have the same slope
y - y1 = m(x - 1)
slope(m) = 1/4
(5,5)...x1 = 5 and y1 = 5
now we sub
y - 5 = 1/4(x - 5) <==== ur parallel line
==================
perpendiculr lines will have a negative reciprocal slope. To find the negative reciprocal, u flip the number and change the sign. So the negative reciprocal of 1/4 is -4....see how I flipped 1/4 and made it 4/1...then changed the sign making it -4/1 or just -4. That will be ur slope of the perpendicular line.
y - y1 = m(x - x1)
slope(m) = -4
(5,5)...x1 = 5 and y1 = 5
now we sub
y - 5 = -4(x - 5) <=== ur perpendicular line
        
             
        
        
        
Answer: 56
Explanation: 28 pounds = 448 ounces 
448/8=56