# Math Help - Trigonometric functions

1. ## Trigonometric functions

The function y=sin(x-p)+d has a vertical translation of -3 and passes through the point (pi/6, -2). Determine the values of p and d

My attempt
d= -3
-2= sin (pi/6 - p) -3
1 = 1/2 - sinp
1-1/2= - sinp
1/2= - sinp
-1/2= sinp

The question didn't specify a domain so how would I find the value of p?

2. ## Re: Trigonometric functions

Originally Posted by xoxo
The function y=sin(x-p)+d has a vertical translation of -3 and passes through the point (pi/6, -2). Determine the values of p and d

My attempt
d= -3
-2= sin (pi/6 - p) -3
1 = 1/2 - sinp
note ...

${\color{red}\sin\left(\frac{\pi}{6} - p\right) \ne \sin\left(\frac{\pi}{6}\right) - \sin{p}}$

3. ## Re: Trigonometric functions

-2 = sin ( π/6-p)-3
Or
sin ( π/6-p)=1=sin⁡ π/2
Therefore one of the solution would be
π/6-p = π/2 That gives p = - π/3