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
= \(\frac{2}{√3}\)
11 and 12 Grade Math
From Trigonometrical Ratios of (360° + θ) to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.