When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent?
2 answers:
Note that (5π)/6 radians = 150°. Therefore the given angle is in quadrant 2.
Refer to the figure shown below.
Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2, sin θ' = 1/2, tan θ' = √3.
Because we are in quadrant 2,
sin θ' = π/6;
sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.
Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.
Refer to the figure shown below.
Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2, sin θ' = 1/2, tan θ' = √3.
Because we are in quadrant 2,
sin θ' = π/6;
sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.
Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.
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Explanation
The question indicates we should use a logistic model to estimate the number of plants after 5 months.
This can be done using the formula below;
Workings
Step 1: We would need to get the value of A using the carrying capacity and initial plants that started growing in the yard.
This gives;
Step 2: Substitute the value of A into the formula.
Step 3: Find the value of the constant k
Kindly recall that we are told that the plants increase by 80% after each month. Therefore, after one month we would have;
We can then have that after t= 1month
Step 4: Substitute -k back into the initial formula.
The above model is can be used to find the population at any time in the future.
Therefore after 5 months, we can estimate the model to be;
Answer: The estimated number of plants after 5 months is 130 plants.
Answer:
(x, y) = (-6, -4)
Step-by-step explanation:
The solution can be found quickly using a graphing calculator. It is the point of intersection of the two lines.
_____
If you like, you can solve the system algebraically. The second equation can be rewritten to give ...
y = x +2
Substituting this into the first equation gives ...
5/3x -2(x +2) = -2
-1/3x -4 = -2
Adding 4 and multiplying by -3 gives ...
x = -3(-2+4) = -6
Then our equation for y tells us ...
y = -6 +2 = -4
The solution is (x, y) = (-6, -4).
