Find the number of solutions for
1
2
3
4
Simultaneous Trigonometric Equations -
Simultaneous Trigonometric Equations
We can divide the problems related to Simultaneous Trigonometric Equations into two categories:
If two equations satisfies simultaneously having only one unknown.
If two equations satisfies simultaneously having two unknowns.
Let us go through some illustrations to understand how to solve Simultaneous Trigonometric Equations
Illustrations 1
The most general value of x which satisfies the equation cos x = -½ and cot x = 1/√3.
First, find the value of x which satisfies two given equations separately
cos x = -½ ⇒ x = 2π/3 and 4π/3 [in 0 to 2π]
cot x = 1/√3 ⇒ x = π/3 and 4π/3 [in 0 to 2π]
Now select the value x which satisfies both the equation
Here common value is 4π/3,
Hence, the required solution is x = 2nπ + 4π/3.
Illustrations 2
If two equations given r sin x = 4 and r = 3 sin x - 1, this equation satisfies if -π ≤ x ≤ π , then the possible solution of the pair (r, x) is
Here two equation given r sin x = 4 and r = 3 sin x - 1
Eliminating x from above equation, we get
Now,
Hence the required pair is (-4, -π/2 )
-
Graph -
By the graph we can say the number of solutions for this equation is 3.
Study 40% syllabus and score up to 100% marks in JEE