Matching a trig equation to a given situation

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Math_Junkie

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The temperature (T, in degrees C) at Timbuktu varies in a sinusoidal manner over a year, reaching a maximum of 23 on July 18, and a minimum of 9 on January 18. Identify the equation that most closely represents the temperature as a function of time t, where t is counted in years beginning Jan 1. (e.g. Jan 1 is t=0, July 1 is t=0.5).

a) T(t)=16+7cos(2?(t-0.55))
b) T(t)=16-7sin(2?(t+0.55))
c) T(t)=16+7sin(2?(t-0.05))
d) T(t)=16+7sin(2?(t-0.30))
e) T(t)=16+7cos(2?(t+0.55))
f) None of the above.

Is it none of the above? I can't seem to see how any of the choices listed works with the situation.

Thanks for any help/clarification. :)
 
Math_Junkie said:
The temperature (T, in degrees C) at Timbuktu varies in a sinusoidal manner over a year, reaching a maximum of 23 on July 18, and a minimum of 9 on January 18. Identify the equation that most closely represents the temperature as a function of time t, where t is counted in years beginning Jan 1. (e.g. Jan 1 is t=0, July 1 is t=0.5).

a) T(t)=16+7cos(2?(t-0.55))
b) T(t)=16-7sin(2?(t+0.55))
c) T(t)=16+7sin(2?(t-0.05))
d) T(t)=16+7sin(2?(t-0.30))
e) T(t)=16+7cos(2?(t+0.55))
f) None of the above.

Is it none of the above? I can't seem to see how any of the choices listed works with the situation.

Thanks for any help/clarification. :)
Click to expand...

Remember - your problem stated "most closely" - not exactly.
 
Math_Junkie said:
Then would the answer be c)? (purely guessing by imagining the graph)
Click to expand...

Why imagine - plot those with a graphing software and and then guess....
 
Thanks for the suggestion. I graphed all the functions and I'm stuck between a and d. They seem to be identical.

Would the correct answer be d) since the question specifies it's a sinuosidal function?
 
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