a.
To explain: Why the value of
For any sign change of
Given information:
Sinusoidal equation is given by,
Calculation:
Considering the equation,
It is noted that the sine function is odd from the given equation.
Therefore, for any sign change of
b.
To prove: The equation
Given information:
The given equations are,
Proof:
Since a sine curve is identical to a cosine curve offset to the right by
Rewriting the above cosine curve in terms of a sine function,
c.
To graph: The unit circle argument for the identity
Given information:
The identity is given by
Graph:
From the given identity,
Interpretation:
The graph indicates the arbitrary angle
d.
To prove: The equation
Given information:
The given equations are,
Proof:
Consider the two given identities and relating both to get,
Substitute
If
Therefore, both the identity has the same graph for the chosen value
e.
To prove: Any sinusoid can be represented
Given information:
The given equations are,
Proof:
Comparing all the results from part (a) to (d), it is known that,
The equation includes all requirements for vertical shifting
Therefore, for any sinusoid it can be represented by the equation
Chapter 4 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- For each function, identify all points of discontinuity and label them as removable, jump, or infinite. A) f(x) = x-4 (X+15)(x-4) B) f(x) = (x²-1 x ≤2 14-2x 2arrow_forwardFind the one sided limit 2 lim Flx) where f(x) = (x²-4_xarrow_forwardRequired information A telephone cable is clamped at A to the pole AB. The tension in the left-hand portion of the cable is given to be T₁ = 815 lb. T₁ 15° A 25° T₂ I B Using trigonometry, determine the corresponding magnitude of R. The corresponding magnitude of R is lb.arrow_forwardTwo forces are applied as shown to a hook support. The magnitude of P is 38 N. 50 N 25° DC a Determine the corresponding magnitude of R. The magnitude of R is N.arrow_forwardLet y(t) represent your retirement account balance, in dollars, after t years. Each year the account earns 7% interest, and you deposit 8% of your annual income. Your current annual income is $34000, but it is growing at a continuous rate of 2% per year. Write the differential equation modeling this situation. dy dtarrow_forwardDetermine Whether series converge or diverge if it converge what is the limit. $\{ \frac {(-1)^{n-2}n^{2}}{4+n^{3}}\} _{n=0}^{\infty }$arrow_forwardLet y(t) represent your retirement account balance, in dollars, after t years. Each year the account earns 7% interest, and you deposit 8% of your annual income. Your current annual income is $34000, but it is growing at a continuous rate of 2% per year. Write the differential equation modeling this situation. dy dtarrow_forward8:37 ▬▬▬▬▬▬▬▬▬ Ο Graph of f The figure shows the graph of a periodic function f in the xy-plane. What is the frequency of f? 0.5 B 2 C 3 D 8 3 of 6 ^ Oli Back Next apclassroom.collegeboard.orgarrow_forward2. The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given by f(t)=5000.1 Under certain storage conditions, where t is time in days after packing of the product and the value of f(t) is in millions. The solution to word problems should always be given in a complete sentence, with appropriate units, in the context of the problem. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take? (b) If t=0 corresponds to January 1, what date should be placed on the product?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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