Question

For which value of theta is sin theta equals -1?

Answer 1

The value of theta is sin theta equals -1 is:

`\theta=(3\pi)/(2)`

Explanation:

We know that on this magic circle with radius 1, the coordinates of the points are nothing but:

(cosθ,sinθ)

Now, based on this unit circle we see that the angle for which the second coordinate of the point is -1 is:

`\theta=(3\pi)/(2)`

( The point is: (0,-1) and this point is obtained corresponding to the angle 3π/2.

and at this angle we have:

cosθ=0

and sinθ=-1 )

Answer 2

The value of Ф is 3π/2

Explanation:

* Lets revise the angle Ф in the four quadrant

∵ r = √(x² + y²) ⇒ square the two sides

∴ x² + y² = r²

∵ r = 1

∴ x² + y² = 1

∵ cos² Ф + sin² Ф = 1

∵ x is the adjacent side to Ф and y is the opposite side to Ф

∴ x = cos Ф and y = sin Ф

- At point (1 , 0)

∵ x = 1 , y = 0

∴ cos Ф = 1 and sin Ф = 0

∵ The positive part of x-axis represents the angle 0 and 2π

∴ cos 0 and 2π are 1 and sin 0 and 2π are 0

- At point (0 , 1)

∵ x = 0 , y = 1

∴ cos Ф = 0 and sin Ф = 1

∵ The positive part of y-axis represent the angle π/2

∴ cos π/2 is 0 and sin π/2 is 1

- At point (-1 , 0)

∵ x = -1 , y = 0

∴ cos Ф = -1 and sin Ф = 0

∵ The negative part of x-axis represents the angle π

∴ cos π is -1 and sin π is 0

- At point (0 , -1)

∵ x = 0 , y = -1

∴ cos Ф = 0 and sin Ф = -1

∵ The negative part of y-axis represent the angle 3π/2

∴ cos 3π/2 is 0 and sin 3π/2 is 1

* For the value of Ф = 3π/2 is sin Ф = -1