Table of Contents
What is the general solution of Sinx 1 2?
Trig table gives sinx=12=sin(π6)−→x1=π6 . Trig circle gives another arc x2=5π6 that has the same sin value (12) .
Which angle has a sin value of 1 2?
Sines and cosines for special common angles
| Degrees | Radians | sine |
|---|---|---|
| 60° | π/3 | √3 / 2 |
| 45° | π/4 | √2 / 2 |
| 30° | π/6 | 1/2 |
| 0° | 0 | 0 |
What is a principle solution?
Solving an equation means to find the set of all values of the unknown value which satisfy the given equation. The solutions lying between 0 to 2π or between 0° to 360° are called principal solutions.
What is the principal solution of Sinx?
Solutions for Trigonometric Equations. Let us begin with a basic equation, sin x = 0. The principal solution for this case will be x = 0, π, 2π as these values satisfy the given equation lying in the interval [0, 2π].
What is principal solution architect?
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How do you find the principal and general solution of trig equations class 11?
- Principal and General Solution.
- Principal solutions: The solutions where 0 ≤ x < 2π.
- General solution: The expression involving integer ‘n’ this gives all solutions of a trigonometric equation.
- Theorem 1: For any real numbers x and y, sin x = sin y implies x = nπ + (–1)n y, where n ∈ Z.
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.
How do you find the absolute value of sin x?
The absolute value is the distance between a number and zero. The distance between 0 0 and 1 1 is 1 1. Divide 2 π 2 π by 1 1. The period of the sin(x) sin ( x) function is 2π 2 π so values will repeat every 2π 2 π radians in both directions.
What is the value of sin 270 + sin 360?
As sin 270 is -1 and sin 360 is 0. Now as obvious as it seems, we take the mean of the two angles because: Hence the answer you were looking for is x = 315. Well this may seem a little foolish hence we can prove is graphically using the sine curve.
What is the exact value of arcsin(1 2)?
The exact value of arcsin(1 2) arcsin ( 1 2) is π 6 π 6. The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from π π to find the solution in the second quadrant. Simplify π − π 6 π – π 6. Tap for more steps…