Loading [MathJax]/jax/output/HTML-CSS/jax.js

Problems on Trigonometric Equation

We will learn how to solve different types of problems on trigonometric equation containing one or many trig functions. First we need to solve the trigonometric function (if required) and then solve for the angle value using the trigonometric equation formulas.

1. Solve the equation sec θ - csc θ = 4/3

Solution:

sec θ - csc θ = 4/3

1cosθ - 1sinθ = 4/3

sinθcosθsinθcosθ = 4/3

⇒ 3 (sin θ - cos θ) = 4 sin θ cos θ

⇒ 3 (sin θ - cos θ) = 2 sin 2θ

⇒ [3 (sin θ - cos θ)]2 = (2 sin 2θ)2, [Squaring both sides]

⇒ 9 (sin2 θ - 2 sin θ cos θ + cos2 θ) = 4 sin2

⇒ 9 (sin2 θ + cos2 θ - 2 sin θ cos θ) = 4 sin2

⇒ 9 (1 - 2 sin θ cos θ) = 4 sin2

⇒ 4 sin2 2θ + 9 sin 2θ - 9 = 0

⇒ (4 sin 2θ - 3)(sin 2θ + 3) = 0

⇒ 4 sin 2θ - 3 = 0 or sin 2θ + 3 = 0

⇒ sin 2θ = ¾ or sin 2θ = -3

but sin 2θ = -3 is not possible.

Therefore, sin 2θ = ¾ = sin ∝ (say)

⇒ 2θ =  nπ + (-1)n ∝, where, n = 0, ± 1, ± 2, ± 3, ± 4 ..... and sin ∝ = ¾

⇒ θ = nπ2 + (-1)n 2, where, n = 0, ± 1, ± 2, ± 3, ± 4 ..... and sin ∝ = ¾

Therefore, the required solution θ = nπ2 + (-1)n 2, where, n = 0, ± 1, ± 2, ± 3, ± 4 ..... and sin ∝ = ¾


2. Find general solution of the equation cos 4θ = sin 3θ.

Solution: 

cos 4θ = sin 3θ                                  

⇒ cos 4θ = cos (π2 - 3θ)

Therefore, 4θ = 2nπ ± (π2 - 3θ) 

Therefore, either 4θ = 2nπ + π2 - 3θ Or, 4θ = 2nπ - π2 + 3x

⇒ 7θ = (4n + 1)π2 or, θ = (4n - 1)π2

⇒ θ = (4n + 1)π14 or, θ = (4n - 1)π2

Therefore the general solution of the equation cos 4θ = sin 3θ are θ = (4n + 1)π14and θ = (4n - 1)π2 , where, n = 0, ±1, ±2, …………………..

 Trigonometric Equations




11 and 12 Grade Math

From Problems on Trigonometric Equation 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

  1. Construction of Bar Graphs | Examples on Construction of Column Graph

    Jul 30, 25 03:20 PM

    What is Bar Graph?
    Now we will discuss about the construction of bar graphs or column graph. In brief let us recall about, what is bar graph? Bar graph is the simplest way to represent a data. In consists of rectangular…

    Read More

  2. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  3. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  4. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  5. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More