Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.
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
= 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
From Trigonometrical Ratios of (360° + θ) to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.