Question

Which trigonometric function requires a domain restriction of [-pi/2,pi/2]?

Answer 1

The sine trigonometric function requires a domain restriction of [-π/2,π/2] due to the range of the angle x. It relates the length of the side opposite to an angle to the length of the hypotenuse in a right triangle.

Step-by-step explanation:

The trigonometric function that requires a domain restriction of [-π/2,π/2] is the sine function.

Trigonometric functions are mathematical functions that relate angles of a triangle to the lengths of its sides. The sine function, denoted as sin(x), gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse in a right triangle. The domain restriction of [-π/2,π/2] limits the values of the angle x to the range between -π/2 and π/2, which corresponds to the first and fourth quadrants of the unit circle.

For example, if we take the angle x = π/4, the sine function sin(π/4) gives us the ratio of the length of the side opposite to π/4 in a right triangle to the length of the hypotenuse.

Answer 2

The trigonometric function which requires a domain restriction of {-π/2,π/2}

is tan x , sec x

tan x = (sin x)/(cos x) and sec x = 1/(cos x)

cos x becomes zero at {-π/2,π/2}

see the attached figure
tan x ⇒⇒⇒ blue graph
sec x ⇒⇒⇒ red graph
as shown both of the function undefined at {-π/2,π/2}