Posted by **DK** on Monday, May 4, 2009 at 7:21pm.

Scientists believe that the average temperature at various places on Earth vary from cooler to warmer over thousands of years of gradual climate change. Suppose that at one place, the highest avg temp is 80 and the lowest is 60. Also suppose that the time it takes to go from the high to the low average is 20,000 years and in the year 2000 the avg temp is at a high point of 80. How can we use a sinusoidal expression to model this phenomenon?

My work:

So far I have

y=10sin(pi/20,000(x-d))+70

How do I get d? Can someone clearly explain to me how to get the phase shift? thanks

- trig -
**Reiny**, Monday, May 4, 2009 at 8:00pm
make use of the fact that if

x = 2000 , y = 80

80 = 10sin(pi/20000(2000-d))+70

10 = 10sin(pi/20000(2000-d))

1 = sin(pi/20000(2000-d))

so (pi/20000(2000-d)) = pi/2

(2000-d)/10000 = 1

2000-d = 10000

d = -8000

so your equation is

y=10sin(pi/20000(x+8000))+70

(check: sub in x = 2000, it works

y = 80)

- trig -
**DK**, Monday, May 4, 2009 at 8:21pm
When I sub in x=2000, I get y=82.88 on my calculator?

How do I solve it to get 80?

- trig -
**DK**, Monday, May 4, 2009 at 8:23pm
NVM, I got it

Thank you for your help!

## Answer this Question

## Related Questions

- social study - A comparison of the average temperatures on any given day at ...
- Calc - Recent studies indicate that the average surface temp. of the earth has ...
- Science - According to the fossil record shown, how did the Bighorn Basin ...
- grammar - Can some read the paragraph below and check my grammars are correct. ...
- Geogeaphy - The higher the latitude the ( cooler, warmer) the temperature will ...
- Earth Science - Why is it generally warmer in a rural area than in an urban area...
- Science - what are some possible effects of climate change resulting from a ...
- calculus - Some scientists believe that the average surface temperature of the ...
- Applied Math - Cosine Periods) - Trying to decypher something, and am getting ...
- physics - Suppose a simple pendulum is used to measure the acceleration due to ...