Question Details

What is the value of tan 570°?

Options

A

3

B

3

C

13

D

13

Show Answer

Correct Answer :

Option D

13

Solution :

The correct option is 13.

To find the value of tan(570°), we can first express the angle 570° in terms of a complete revolution (360°).

570°=360°+210°

Since the tangent function is periodic with a period of 360° (or 180°), we have:

tan(570°)=tan(360°+210°)=tan(210°)

Next, we rewrite 210° as 180°+30°:

tan(210°)=tan(180°+30°)

Using the trigonometric identity tan(180°+θ)=tan(θ), where θ=30°, we get:

tan(180°+30°)=tan(30°)

The standard trigonometric value for tan(30°) is:

tan(30°)=13

Therefore, the value of tan(570°) is 13.

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