# sin θ = -1

How to find the general solution of an equation of the form sin θ = -1?

Prove that the general solution of sin θ = -1 is given by θ = (4n - 1)π/2, n ∈ Z.

Solution:

We have,

sin θ = -1

⇒ sin θ = sin (-π/2)

θ = mπ + (-1)^m ∙ (-π/2), m ∈ Z, [Since, the general solution of sin θ = sin ∝ is given by θ = nπ + (-1)^n ∝, n ∈ Z.]

θ = mπ + (-1)^m ∙ π/2

Now, if m is an even integer i.e., m = 2n (where n ∈ Z) then,

θ = 2nπ - π/2

⇒ θ = (4n - 1) π/2 …………………….(i)

Again, if m is an odd integer i.e. m = 2n + 1 (where n ∈ Z) then,

θ = (2n + 1) ∙ π + π/2

⇒ θ = (4n + 3) π/2 …………………….(ii)

Now combining the solutions (i) and (ii) we get, θ = (4n - 1)π/2, n ∈ Z.

Hence, the general solution of sin θ = -1 is θ = (4n - 1)π/2, n ∈ Z.

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. ### Worksheet on Triangle | Homework on Triangle | Different types|Answers

Jun 21, 24 02:19 AM

In the worksheet on triangle we will solve 12 different types of questions. 1. Take three non - collinear points L, M, N. Join LM, MN and NL. What figure do you get? Name: (a)The side opposite to ∠L…

2. ### Worksheet on Circle |Homework on Circle |Questions on Circle |Problems

Jun 21, 24 01:59 AM

In worksheet on circle we will solve 10 different types of question in circle. 1. The following figure shows a circle with centre O and some line segments drawn in it. Classify the line segments as ra…

3. ### Circle Math | Parts of a Circle | Terms Related to the Circle | Symbol

Jun 21, 24 01:30 AM

In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

4. ### Circle | Interior and Exterior of a Circle | Radius|Problems on Circle

Jun 21, 24 01:00 AM

A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known