# 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, …………)

Trigonometric Equations

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 1. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 01, 23 01:16 AM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

2. ### Days of the Week | 7 Days of the Week | What are the Seven Days?

Nov 30, 23 10:59 PM

We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…