Trigonometrical Ratios of (360° - θ)

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

• 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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