# transformations of trigonometric graphs

• August 3rd 2010, 04:11 PM
transformations of trigonometric graphs

h = Hcos (tπ/6)

Find t when h = 2.5
H = 3 (height of the high tide in meters)
T = 12

a high tide of 3m occurs at 10am

so I went

2.5 = 3cos (tπ/6)
2.5/3 = cos (tπ/6)

0.833= cos (tπ/6)
Then you take cos^-1 (0.833)
= 33.65/180 x 23 = 4.3 (to convert to hours)

4.3 x 6 = tπ
25.8/π = t

t = 8.21

Yeah I think I'm doing it wrong =(
Thanks for any help.
• August 3rd 2010, 05:51 PM
sa-ri-ga-ma
Then you take cos^-1 (0.833)
= 33.65/180 x 23 = 4.3

From where did you get 23?

Actually 33.65 = t*π/6 = t*180/6.

Now find t.
• August 4th 2010, 06:37 AM
HallsofIvy
Quote:

h = Hcos (tπ/6)

Find t when h = 2.5
H = 3 (height of the high tide in meters)
T = 12

a high tide of 3m occurs at 10am

so I went

2.5 = 3cos (tπ/6)
2.5/3 = cos (tπ/6)

0.833= cos (tπ/6)
Then you take cos^-1 (0.833)
= 33.65/180 x 23 = 4.3 (to convert to hours)

If you intended to convert from degrees to radians, then it is $]33.64(\pi/180)$ not "23"! Of course, once you have $\pi t/6= (33.64/180)\pi$ you can just cancel the " $\pi$s": $t/6= 33.64/180$ so that $t= 33.64/30$.

But since you knew the argument of cosine was in radians (the only time you use degrees is in problems specifically dealing with triangles in which the angles are given in degrees) it would be simpler to set your calculator to "degree" mode.

Quote:

4.3 x 6 = tπ
25.8/π = t

t = 8.21

Yeah I think I'm doing it wrong =(
Thanks for any help.
• August 4th 2010, 12:58 PM