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. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Oct 04, 24 09:47 AM

    Place Value of 3-Digit Numbers
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  2. Worksheet on Subtraction | Practice the Questions | Free Answers

    Oct 04, 24 01:28 AM

    In worksheet on subtraction, all grade students can practice the questions on subtracting numbers with more than two digits. This exercise sheet on subtraction can be practiced by the students

    Read More

  3. Subtraction Word Problems - 2-Digit Numbers | Subtraction Problems

    Oct 03, 24 03:22 PM

    Understand the concept on subtraction word problems - 2-digit numbers for the second grade. Read the question carefully to subtract the two-digit numbers to find the differences and follow the

    Read More

  4. Worksheet on Checking Subtraction Using Addition | Free Answers | Math

    Oct 03, 24 02:22 PM

    Checking Subtraction using Addition
    Here we can use addition to check the answer for the subtraction. Subtract ans check your answer. Find the difference and check your answer using addition.

    Read More

  5. Check for Subtraction and Addition | Checking Subtraction | Problems

    Oct 03, 24 01:13 PM

    Checking Subtraction with Addition
    We will learn to check for subtraction and addition answers after solving. Difference of two numbers is correct when the sum of the subtrahend number and the difference is equal to the minuend.

    Read More