Question

"True or false? Explain. sin(x + pi/2) = cos(x) for all x"

There are nine more like this, but I'll stick with one for now. I'm sure there's a method for determining it, but I don't know what it is. Can anyone explain to me how to figure out whether this is true or false?

Answer 1

True, this is an identity.

Answer 2

The method to determine this is a `sin(a+b)` rule.

\(\large\color{midnightblue}{ \rm sin(x + pi/2) = cos(x) }\) will translate into degres, looks better :)
\(\large\color{midnightblue}{ \rm sin(x + 90) = cos(x) }\)
\(\large\color{midnightblue}{ \rm sin(x)cos(90)+sin(90)cos(x) = cos(x) }\)
\(\large\color{midnightblue}{ \rm sin(x)\times 0+1\times cos(x) = cos(x) }\)
\(\large\color{midnightblue}{ \rm 1\times cos(x) = cos(x) }\)
\(\large\color{midnightblue}{ \rm cos(x) = cos(x) }\)

Answer 3

Ok, I think I've got most of that explanation down. But can you clarify how you got from sin(x)cos(90)+sin(90)cos(x)=cos(x) to this sin(x)×0+1×cos(x)=cos(x) ?

Answer 4

Knowing that \(\large\color{magenta}{ \rm cos(90º ) = 0 }\) and \(\large\color{magenta}{ \rm sin(90º) = 1 }\)

Answer 5

Ooohh, I see now! Thank you so much!

Ok, one more question: Should I use degrees for similar problems like this to make it easier? I can see how it makes this problem much easier, but I want to make sure that I won't screw something up if I do so.

Answer 6

I am 100% sure :)

Answer 7

Great! Thank you so much, I really appreciate it. :D

Answer 8

Anytime:)