What is the principal solution of Cos 1 2?

π/3
Therefore, principal value of cos-1(1/2) = π/3.

How do you find the general solution of cosine?

Similarly, general solution for cos x = 0 will be x = (2n+1)π/2, n∈I, as cos x has a value equal to 0 at π/2, 3π/2, 5π/2, -7π/2, -11π/2 etc.

What is the value of cos x 1 2?

π3
The exact value of arccos(12) arccos ( 1 2 ) is π3 . The cosine function is positive in the first and fourth quadrants.

What is the value of x if cos x 1 2?

If cos x = 1/2, then x = ±60 deg. or ± Π/3.

How do you find the principal solution?

If the equation involves a variable 0 ≤ x < 2π, then the solutions are called principal solutions. A general solution is one which involves the integer ‘n’ and gives all solutions of a trigonometric equation.

What is the principal value of Cos 1?

cos y = cos (2π/3). Thus, the Range of the principal value of cos-1 is [0, π ].

How do you find the principal solution and general solution?

If the equation involves a variable 0 ≤ x < 2π, then the solutions are called principal solutions. A general solution is one which involves the integer ‘n’ and gives all solutions of a trigonometric equation. Also, the character ‘Z’ is used to denote the set of integers.

What is the value of cos theta =- 1?

The exact value of arccos(−1) is π . The cosine function is negative in the second and third quadrants.

What is the value of x if cos x 1?

1 Expert Answer 1) In the unit circle the x represent the cosine of the function and the y represent the sine of the trigonometric function. 2) Looking at the unit circle I noticed that cos(x) =1, corresponds to 360°. in other words cos (360º) =1, the answer is x=360º or x=2π radians.

What is the general solution of cos theta?

cos θ = cos ∝ θ = 2nπ ± ∝, where n ∈ Z. Hence, the general solution of cos θ = cos ∝ is θ = 2nπ ± ∝, where n ∈ Z. Note: The equation sec θ = sec ∝ is equivalent to cos θ = cos ∝ (since, sec θ = 1cosθ and sec ∝ = 1cos∝). Thus, sec θ = sec ∝ and cos θ = cos ∝ have the same general solution.

How do you find the general solution of Class 11?

General solution: The expression involving integer ‘n’ this gives all solutions of a trigonometric equation. To derive general solution we will use the fact that: Values of sinx repeat after an interval of 2π Values of cos x repeat after an interval of 2π

What is the principal solution for sin x = ½?

Principal solution for sin x = ½. sin x = ½. Here sin is positive, We know that. sin is positive in 1st and 2nd quadrant. Value in 1st Quadrant = 30°. Value in 2nd Quadrant = 180° – 30° = 150°. So, Principal solutions are. x = 30° = 30° × π/180 = π/6.

What is the period of the cos(x) cos function?

The period of the cos(x) cos ( x) function is 2π 2 π so values will repeat every 2π 2 π radians in both directions.

How do you find the cosine function in the 4th quadrant?

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from 2π 2 π to find the solution in the fourth quadrant. Simplify 2π− π 4 2 π – π 4. Tap for more steps… To write 2 π 1 2 π 1 as a fraction with a common denominator, multiply by 4 4 4 4.

How to find the general solution of a trigonometric equation?

Find the value of the angle using the positive value. General Solution: The expression involving integer n which gives all solutions of a trigonometric equation is called the general solution. We shall use ‘Z’ to denote the set of integers. 1. Obtain the equation in the form given above