CPhill

Sine and cosine are co-functions.....

sin (90- theta)  =  cos(theta)

sin (90-73)  = cos(73)

sin (16°)  =  cos (73°)

For the second one, we are given an angle, the hypotenuse and we are trying to find the adjacent side......the cosine seems appropriate

cos (39)  = x / 17   multiply both sides by 17

17 * cos(39)  = x  ≈  13.2 m

We know the adjacent side = 15 and the hypotenuse  = 29

So....we can use the cosine inverse to find x

arccos (15/29)  = x  ≈   58.85°

I count 19, tertre........

See what you think....

I  assume this  is :

3^{x + 3}  =  7776         and we can write

3^3 * 3^x  = 7776         divide both sides by 3^3  = 27

3^x   =  288             take the log of both sides

log 3^x   = log (288)     and we can write

x * log 3  =  log (288)       divide both sides by log 3

x  =  log (288)  / log (3)   ≈  5.155

Post the problem......it's hard to tell what you're referrring to.......

I like your first answer, guest.....a very intuitive twist on Gauss....!!!

Well......I didn't spell it at all.......LOL!!!!!!!

200ml x 6 times a day x 7 days per week  =

200ml  x 42   =

8400ml  per week  =   8.4 L  per week

9sec^2 (x)  tan(x)   -  12tan (x)   = 0       re-write as

9tan (x) sec^2 (x)  - 12 tan (x)   =   0

Factor out the greatest common factor,   3tan(x)

3tan (x)  [ 3 sec^2 (x)  - 4  ]  = 0

We need to find the radius

Circumference  = 2 * 3.14 * radius

 7.85  =  2 * 3.14 * radius                divide both sides by  2 * 3.14  =  6.28

[7.85 / 6.28 ] m   =  radius

And the area, A, is given by :

A  =  3.14 * radius^2    =   3.14 * [ 7.85 / 6.28]^2   ≈  4.91 m^2