Answer:
C = 64.145º
Step-by-step explanation:
The Law of Sines is as follows:
=
=
The problem can be draw as the picture attached.
Now, the values of the sides and angles can be substituted into the Law of Sines, and because all parts are equal, only two are needed:
=
Next, cross-multiply:
7sin40º = 5sinC
Then, divide both sides by 5:
= sinC
Finally, take the inverse sin of the left side and convert into a decimal:
C = (
)
C = 64.145
The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.
Reasons:
The given parameters are;
The variation of the height of the tip of the hour hand = 9 feet to 10 feet
At t = 0, the time = 12.00 a.m.
Required: The equation that can be used to model the height as a function of time.
Solution:
The general form of the cosine function is presented as follows;
y = a·cos(b·x - c) + d
The amplitude = a
Therefore;
b = The cycle speed
The period, T, is given as follows;
The period of a block, T = 12 hours
Therefore;
At t = 0, H = The highest point = 10 ft.
Which gives;
-c = arcos(1) = 0
-c = 0
c = 0
The equation is therefore;
The above equation is the same as; <u>H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5</u>
Learn more about the cosine function here: