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










11 and 12 Grade Math

From sin 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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More