Question

Look at the unit circle shown below.

Which statement is TRUE? A The x-coordinate of P corresponds to cosθ , which has a period of 2π . B The x-coordinate of P corresponds to cosθ , which has a period of π . C The y-coordinate of P corresponds to cosθ , which has a period of 2π . D The y-coordinate of P corresponds to cosθ , which has a period of π .

Answer 1

A is true.

Explanation:

Cos θ = adjacent / hypotenuse = x/1 = x.

Cosθ has a period pf 2π.

Answer 2

The correct option is A.

Explanation:

Draw a perpendicular form point P on x-axis.

Radius of unit circle is 1 . It means in triangle OPA

Hypotenuse = OP = 1 units

Adjacent= OA = x

Perpendicular = PA = y

In a circle angled triangle,

`\cos \theta = (adjacent)/(hypotenuse)`

In triangle OPA,

`\cos \theta = (x)/(1)`

`\cos \theta =x`

The x-coordinate of P corresponds to cosθ.

The period of a unit circle is 2π.

Therefore, the correct option is A.