Principal Inverse Values

Front

What is the principal value of an angle in radians?

Back

The principal value of an angle in radians is the unique angle within the range of 0 to 2π that corresponds to a given trigonometric function value.

Front

How do you find the principal value of sin(x) = 1/2?

Back

The principal value of sin(x) = 1/2 is π/6, as it is the angle in the first quadrant where the sine function equals 1/2.

Front

What is the principal value of cos(x) = -1/2?

Back

The principal value of cos(x) = -1/2 is 2π/3, as it is the angle in the second quadrant where the cosine function equals -1/2.

Front

What is the principal value of tan(x) = -√3?

Back

The principal value of tan(x) = -√3 is -π/3, as it is the angle in the fourth quadrant where the tangent function equals -√3.

Front

What is the range of the principal values for trigonometric functions?

Back

The range of principal values for trigonometric functions is typically from 0 to 2π for sine and cosine, and from -π/2 to π/2 for tangent.

Front

How do you determine the principal value of an angle given in degrees?

Back

To determine the principal value of an angle given in degrees, convert the angle to radians and then find the equivalent angle within the range of 0 to 2π.

Front

What is the principal value of sin(x) = -1/2?

Back

The principal value of sin(x) = -1/2 is 7π/6, as it is the angle in the third quadrant where the sine function equals -1/2.

Front

What is the significance of the principal value in trigonometry?

Back

The principal value is significant in trigonometry as it provides a standard reference angle for solving equations and understanding the behavior of trigonometric functions.

Front

How do you find the principal value of cos(x) = 1/2?

Back

The principal value of cos(x) = 1/2 is π/3, as it is the angle in the first quadrant where the cosine function equals 1/2.

Front

What is the principal value of tan(x) = 1?

Back

The principal value of tan(x) = 1 is π/4, as it is the angle in the first quadrant where the tangent function equals 1.