tell me general solutions of where sin theta is 0,1,-1 and same with cos theta and same with tan,cot Flashcards
(21 cards)
Where is sin(theta) equal to 0?
sin(theta) = 0 at theta = nπ, where n is any integer.
Where is sin(theta) equal to 1?
sin(theta) = 1 at theta = π/2 + 2nπ, where n is any integer.
Where is sin(theta) equal to -1?
sin(theta) = -1 at theta = 3π/2 + 2nπ, where n is any integer.
Where is cos(theta) equal to 0?
cos(theta) = 0 at theta = (2n+1)π/2, where n is any integer.
Where is cos(theta) equal to 1?
cos(theta) = 1 at theta = 2nπ, where n is any integer.
Where is cos(theta) equal to -1?
cos(theta) = -1 at theta = (2n+1)π, where n is any integer.
Where is tan(theta) equal to 0?
tan(theta) = 0 at theta = nπ, where n is any integer.
Where is tan(theta) equal to 1?
tan(theta) = 1 at theta = π/4 + nπ, where n is any integer.
Where is tan(theta) equal to -1?
tan(theta) = -1 at theta = -π/4 + nπ, where n is any integer.
Where is cot(theta) equal to 0?
cot(theta) = 0 at theta = π/2 + nπ, where n is any integer.
Where is cot(theta) equal to 1?
cot(theta) = 1 at theta = π/4 + nπ, where n is any integer.
Where is cot(theta) equal to -1?
cot(theta) = -1 at theta = -π/4 + nπ, where n is any integer.
True or False: Sin(theta) can only take values between -1 and 1.
True.
True or False: Cos(theta) is equal to 1 at odd multiples of π.
False.
Fill in the blank: Tan(theta) is undefined at theta = _____ + nπ/2.
π/2 or 3π/2.
What is the general solution for sin(theta) = 0?
theta = nπ, where n is any integer.
What is the general solution for cos(theta) = 0?
theta = (2n+1)π/2, where n is any integer.
Where does tan(theta) equal to infinity?
tan(theta) approaches infinity at theta = π/2 + nπ, where n is any integer.
What is the period of sin(theta)?
The period of sin(theta) is 2π.
What is the period of cos(theta)?
The period of cos(theta) is 2π.
What is the period of tan(theta)?
The period of tan(theta) is π.
