Explanation:
The given equation is False, so cannot be proven to be true.
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Perhaps you want to prove ...
This is one way to show it:
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We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
The area of the circle is πr², ie. 144π.
The volume of the cilinder is 12×144π = 1728π cm³.
I vote for answer A.
I believe a would be on the first line.
For this case we are going to define the following variable:
x: time in minutes
We write the linear function that represents the problem:
t (x) = (14/4) x + 7
For x = 6 we have:
t (6) = (14/4) * (6) + 7
t (6) = 28 ° C
For x = 11 we have:
t (11) = (14/4) * (11) + 7
t (11) = 45.5 ° C
Answer:
t (6) = 28 ° C
t (11) = 45.5 ° C
