cos θ = -1
How to find the general solution of an equation of the form cos θ = -1?
Prove that the general solution of cos θ = -1 is given by θ = (2n + 1)π, n ∈ Z.
Solution:
We have,
cos θ = -1
⇒ cos θ = cos π
θ = 2mπ ± π, m ∈ Z, [Since, the general solution of cos θ = cos ∝ is given by θ = 2nπ ± ∝, n ∈ Z.]
⇒ θ = (2m ± 1)π, m ∈ Z, (i.e., n = 0, ± 1,± 2, …………)
⇒ θ = odd multiple of π = (2n + 1)π , where n ∈ Z,(i.e., n = 0, ± 1,± 2, …………)
Hence, the general solution of cos θ = -1 is θ = (2n + 1)π, n ∈ Z (i.e., n = 0, ± 1,± 2, …………)
- General solution of the equation sin x = ½
- General solution of the equation cos x = 1/√2
- General solution of the equation tan x = √3
- General Solution of the Equation sin θ = 0
- General Solution of the Equation cos θ = 0
- General Solution of the Equation tan θ = 0
- General Solution of the Equation sin θ = sin ∝
- General Solution of the Equation sin θ = 1
- General Solution of the Equation sin θ = -1
- General Solution of the Equation cos θ = cos ∝
- General Solution of the Equation cos θ = 1
- General Solution of the Equation cos θ = -1
- General Solution of the Equation tan θ = tan ∝
- General Solution of a cos θ + b sin θ = c
- Trigonometric Equation Formula
- Trigonometric Equation using Formula
- General solution of Trigonometric Equation
- Problems on Trigonometric Equation
11 and 12 Grade Math
From cos θ = -1 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.
Recent Articles
-
2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Dec 14, 24 12:25 PM
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. -
Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns
Dec 13, 24 08:43 AM
We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r… -
Patterns in Math | Missing Number | Counting Numbers | Worksheets
Dec 13, 24 12:31 AM
Finding patterns in math is very important to understand the sequence in the series. We need to find the exact missing number that from the group of numbers. The counting numbers may be counting -
Concept of Pattern | Similar Patterns in Mathematics | Similar Pattern
Dec 12, 24 11:22 PM
Concept of pattern will help us to learn the basic number patterns and table patterns. Animals such as all cows, all lions, all dogs and all other animals have dissimilar features. All mangoes have si… -
2nd Grade Geometry Worksheet | Plane and Solid Shapes | Point | Line
Dec 12, 24 10:31 PM
2nd grade geometry worksheet
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.