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Which trigonometric functions are equivalent to sin (theta)? Select all that apply.(2 correct answers)

a.) sin(-theta)
b.) sin(theta +2pi)
c.) -sin(theta)
d.) -sin(-theta)
e.) sin(theta + pi/2)

Respuesta :

laurellee27

Answer:

sin(θ) = sin(θ + 2π) = -sin(-θ)

b and d

This can be shown by substituting a value for θ

sin(π ÷ 3) = 1/2

sin(π ÷ 3 + 2π) = 1/2

-sin(π ÷ 3) = -1/2

-sin(-π ÷ 3) = 1/2

sin(π ÷ 3 + π ÷ 2) = √3/2

The trigonometric functions that are equivalent to sin (theta) are:

(b) sin(theta +2pi)

(d) -sin(-theta)

What are trigonometric function?

"Trigonometric functions are the functions which denote the relationship between angle and sides of a right-angled triangle."

Compound angle formula:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

For given question,

we need to find the trigonometric functions are equivalent to sin (theta).

We know,

a) sin(-theta) = -sin(theta)

sin(-theta) ≠ sin(theta)

b) sin(theta +2pi)

Using compound angle formula,

sin(theta +2pi)

= sin(theta)cos(2π) + cos(theta)sin(2π)

= sin(theta) (1) + cos(theta) (0)

= sin(theta) + 0

= sin(theta)

Therefore, sin(theta +2pi) = sin(theta)

c) -sin(theta) ≠ sin(theta)

d) -sin(-theta)

= -[-sin(theta)]

= sin(theta)

Therefore, -sin(-theta) = sin(theta)

e) sin(theta + pi/2)

Using compound angle formula,

sin(theta + pi/2)

= sin(theta) cos(π/2) + cos(theta)sin(π/2)

= sin(theta)(0) + cos(theta) (1)

= 0 + cos(theta)

= cos(theta)

≠ sin(theta)

Therefore, the trigonometric functions that are equivalent to sin (theta) are:

(b) sin(theta +2pi)

(d) -sin(-theta)

Learn more about trigonometric functions here:

https://brainly.com/question/14746686

#SPJ2

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