For a particular angle theta, the cosine function f(x) = a cos b(theta) has the following values within one cycle of the function: f(0)=4;f(pi/4)=0;f(pi/2)=-4;f(3pi/4)=0;f(pi)=4. What is the rule for the cosine function?
a. y=2cos4theta
b. y=4cos2theta
c. y=-4cos3theta
d. y=1/4cos2theta
huh? Just work with the numbers:
a cos b(theta)
has the following values within one cycle of the function: f(0)=4;f(pi/4)=0;f(pi/2)=-4;f(3pi/4)=0;f(pi)=4
acos(b*0) = 4
so, a=4
4cos(b*pi/2) = -4,
so, b*pi/2 = pi
b = 2
f(θ) = 4cos(2θ)
Thanks steve!
For a particular angle Θ, the cosine function f(x) = a cos b(Θ) has the following values within one cycle of the function:
The figure shows a list of 5 function values.f left parenthesis 0 right parenthesis equals 3 semi colon
f left parenthesis Start fraction pi over 4 End fraction right parenthesis equals 0 semi colon
f left parenthesis Start fraction pi over 2 End fraction right parenthesis equals negative 3 semi colon
f left parenthesis Start fraction 3 pi over 4 End fraction right parenthesis equals 0 semi colon
f left parenthesis pi right parenthesis equals 3
What is the rule for the cosine function?
what is the rule for the cosine function
y=1/3cos 2theta
y=2cos3theta
y=3costheta/2
y=3cos2theta
The correct answer is:
y = 3cos(2θ)
what is the rule for the cosine function Explain
y=1/3cos 2theta
y=2cos3theta
y=3costheta/2
y=3cos2theta
The rule for the cosine function that matches the given values is y = 3cos(2θ).
Within one cycle of the function, the given function values are f(0) = 3, f(π/4) = 0, f(π/2) = -3, f(3π/4) = 0, and f(π) = 3.
If we plug in θ = 0, we get f(0) = 3, which matches one of the given function values.
Next, we can use the fact that the period of the cosine function is 2π to figure out the value of b in the function f(x) = a cos b(Θ). The given points in the cycle are separated by π/2 radians, which means that the period of the function is π/2. The general formula for the period of a cosine function is 2π/b, so we have:
2π/b = π/2
Solving for b, we get b = 4.
Now we can use the point (π/2, -3) to find the value of a:
-3 = 3cos(2(π/2)) = 3cos(π) = -3a
So a = 1.
Putting the two pieces together, we get the rule for the cosine function that matches the given values:
y = 3cos(2θ)