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