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
11 and 12 Grade Math
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