Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
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We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
Answer:
Obtuse and Isosceles
Step-by-step explanation:
Since there is an angle greater than 90 degrees (104 degrees) the triangle is obtuse. Since there are two congruent sides, the triangle is also Isosceles.
Answer:
0.531 (3 s.f.)
Step-by-step explanation:
Power rule is used for the 3rd step.
The solution is when they intersect. So to find the answer, set each equation equal to each and solve:
-2x + 3 = x^2 -6x + 3
3 = x^2 -4x + 3
0 = x^2 -4x
0 = x(x-4)
So the solutions are x = 0 and x = 4
Plug in these values into the easier equation to solve for the y's
x = 0 into -2x + 3 gives y = 3
So one solution is (0, 3)
x = 4 into -2x + 3 gives y = -5
So the second solution is (4, -5)
Answer: Rational, That’s your answer.
