# Trigonometrical Ratios of (360° + θ)

We will find the results of trigonometrical ratios of (360° + θ) and (n ∙ 360° + θ).

If n is a positive integer then the trigonometrical ratios of (n ∙ 360° + θ) are equal to the trigonometrical ratios of (+ θ).

Therefore,

sin (n ∙ 360° +  θ) = sin θ;

cos (n  ∙ 360° +  θ) = cos θ;

tan (n  ∙ 360° +  θ= tan θ;

csc (n ∙ 360° +  θ) = csc θ;

sec (n  ∙ 360° +  θ) = sec θ;

cot (n  ∙ 360° +  θ= cot θ.

Solved examples:

1. Find the value of cos 420°.

Solution:

cos 420° = cos (360 + 60)°

= cos 60°; since we know, cos (n  ∙ 360° +  θ) = cos θ

= 1/2

2. Find the value of tan 405°.

Solution:

tan 405° = tan (360 + 45)°

= tan 45°; since we know, tan (n  ∙ 360° +  θ) = tan θ

= 1

3. Find the value of csc 450°.

Solution:

csc 450° = csc (360 + 90)°

= csc 90°; since we know, csc (n ∙ 360° +  θ) = csc θ

= 1

4. Find the value of sec 390°.

Solution:

sec 390° = sec (360 + 30)°

= sec 30°; since we know, sec (n ∙ 360° +  θ) = sec θ

= $$\frac{2}{√3}$$

Trigonometric Functions