Question

This identity means that translating the basic sine graph Π/2 units to the right produces a cosine graph.
sin(Π/2-x) = cosx

Answer 1

true or false

Answer 2

Draw a right triangle and compare ratios

Answer 3

that other angle is (pi/2-x)
since (pi/2-x)+x must equal pi/2

Answer 4

now find cos(x) and sin(pi/2-x)

Answer 5

and i guess you could always use the difference identity for the sin(pi/2-x)
if you don't like this triangle idea

Answer 6

i think the given statement is wrong
translating sinx to right by pi/2 should give sin(x-pi/2)

Answer 7

Remember that \(\cos = \text{co-sin}\). There the meaning for \(\text{co}\) that \(\text{co}f(x) = f(\pi/2-x)\)

Answer 8

This is why \(\cos(x) = \sin(\pi/2-x)\). It's almost a definition.

Answer 9

didn't read the paragraph above about the identity

Answer 10

I agree with the guru @ganeshie8

Answer 11

now if it had said translating the basic graph of -sin graph pi/2 units to the right produces a cosine graph I might feel better about that

Answer 12

use the fact the sin is odd and that sin and cos are cofunctions

Answer 13

I think let me see

Answer 14

\[-\sin(x-\frac{\pi}{2}) \\ =\sin(-x+\frac{\pi}{2}) =\sin(\frac{\pi}{2}-x)\]

Answer 15

so its a false statement?

Answer 16

yes i would tick false as it is not a direct consequence of that identity

Answer 17

sin(pi/2-x) = cos(x) can be thought of like this :

reflection of sin(x) about y axis and then a translation of pi/2 units to the left