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
