# Trigonometrical Ratios of (360° - θ)

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

If n is a negative 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 sec 300°.

Solution:

sec 300° = sec (360 - 60)°

= sec 60°; since we know, sec (n ∙ 360° -  θ) = sec θ

= 2

2. Find the value of sin 270°.

Solution:

sin 270° = sin (360 - 90)°

= - sin 90°; since we know, sin (n ∙ 360° -  θ) = - sin θ

= - 1

3. Find the value of tan 330°.

Solution:

tan 330° = tan (360 - 30)°

= - tan 30°; since we know, tan (n ∙ 360° -  θ) = - tan θ

= - $$\frac{1}{√3}$$

4. Find the value of cos 315°.

Solution:

cos 315° = cos (360 - 45)°

= cos 45°; since we know, cos (n ∙ 360° -  θ) = cos θ

= $$\frac{1}{√2}$$

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