Trigonometrical Ratios of (360° + θ)

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

• Basic Trigonometric Ratios and Their Names
• Restrictions of Trigonometrical Ratios
• Reciprocal Relations of Trigonometric Ratios
• Quotient Relations of Trigonometric Ratios
  
• Limit of Trigonometric Ratios
  
• Trigonometrical Identity
• Problems on Trigonometric Identities
• Elimination of Trigonometric Ratios
• Eliminate Theta between the equations
• Problems on Eliminate Theta
• Trig Ratio Problems
• Proving Trigonometric Ratios
• Trig Ratios Proving Problems
• Verify Trigonometric Identities
• Trigonometrical Ratios of 0°
• Trigonometrical Ratios of 30°
• Trigonometrical Ratios of 45°
• Trigonometrical Ratios of 60°
• Trigonometrical Ratios of 90°
• Trigonometrical Ratios Table
• Problems on Trigonometric Ratio of Standard Angle
  
• Trigonometrical Ratios of Complementary Angles
• Rules of Trigonometric Signs
• Signs of Trigonometrical Ratios
  
• All Sin Tan Cos Rule
• Trigonometrical Ratios of (- θ)
• Trigonometrical Ratios of (90° + θ)
• Trigonometrical Ratios of (90° - θ)
• Trigonometrical Ratios of (180° + θ)
• Trigonometrical Ratios of (180° - θ)
• Trigonometrical Ratios of (270° + θ)
• Trigonometrical Ratios of (270° - θ)
• Trigonometrical Ratios of (360° + θ)
• Trigonometrical Ratios of (360° - θ)
• Trigonometrical Ratios of any Angle
• Trigonometrical Ratios of some Particular Angles
• Trigonometric Ratios of an Angle
• Trigonometric Functions of any Angles
• Problems on Trigonometric Ratios of an Angle
• Problems on Signs of Trigonometrical Ratios

11 and 12 Grade Math

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