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प्रश्न
From the curve y = sin x, graph the function
y = `sin (pi/2 - x)` which is also cos x (refer trigonometry)
उत्तर
y = sin x
| x | 0 | `pi/2` | π | `3 pi/2` | 2π | `- pi/2` | – π | `- 3 pi/2` | – 2π |
| y | 0 | 1 | 0 | – 1 | 0 | – 1 | 0 | 1 | 0 |
x = 0 ⇒ y = `sin (pi/2 - 0) = sin pi/2` = 1
x = `pi/2` ⇒ y = `sin (pi/2 - pi/2)` = sin 0 = 0
x = π ⇒ y = `sin (pi/2 - pi) = sin(- pi/2) = - sin pi/2` = – 1
x = `3 pi/2` ⇒ y = `sin (pi/2 - 3 pi/2)` = sin (– π) = – sin π = 0
x = 2π ⇒ y = `sin (pi/2 - 2pi) = sin(- 3 pi/2) =- sin 3 pi/2 = - sin (pi + pi/2) = sin pi/2` = 1
x = `- pi/2` ⇒ y = `sin (pi/2 + pi/2)` = sin π = 0
x = – π ⇒ y = `sin (pi/2 + pi) = - sin pi/2` = – 1
x = `- 3 pi/2` ⇒ y = `sin (pi/2 + 3 pi/2)` = sin 2π = 0
x = – 2π ⇒ y = `sin (pi/2 + 2pi) = sin pi/2` = 1
| x | 0 | `pi/2` | π | `3 pi/2` | 2π | `- pi/2`` | – π | `3 pi/2`` | – 2π |
| y | 1 | 0 | – 1 | 0 | 1 | 0 | – 1 | 0 | 1 |
The graph of `sin (pi/2 - x)` causes the graph y = sin x a shift to the right by `pi/2` unit.
The graph of y = f(x – c), c > 0 causes the graph y = f(x) a shift to the right by c units.
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