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
= \(\frac{1}{√2}\)
11 and 12 Grade Math
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