1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π?
2. what trig function never crosses the x-axis and has a value of 2 at π/6?
are these correct?
3. what trig function has a period of π and is undefined for -π/2, π/2, 3π/2...
answer: y=tan x?
4. what trig function has a period of 2π, is continuous, and is increasing for 0 < x < π/2?
answer: y=sin x?
1. An amplitude of 1 applies to only the sine or cosine function.
the given domain puts the angle in the 2nd quadrant.
in that quad, the sine is positive and the cosine is negative, so it has to be
y = cosx
2. I know that sin30° = sin(π/6) = 1/2
so csc (π/6) = 2
and we know that the cosecant has values ≥1 or ≤-1 , never crossing the x-axis
so y = cscx
3. you are correct
4. you are correct
1. The trig function that has an amplitude of 1 and negative values for angles between π/2 and π is the sine function (sin(x)).
2. The trig function that never crosses the x-axis and has a value of 2 at π/6 is the secant function (sec(x)).
3. No, the trig function with a period of π and undefined for -π/2, π/2, 3π/2... is the secant function (sec(x)). The tangent function (tan(x)) is undefined for π/2, 3π/2, 5π/2...
4. Yes, the trig function with a period of 2π, continuous, and increasing for 0 < x < π/2 is the sine function (sin(x)).
1. You are correct! The trig function that has an amplitude of 1 and negative values for angles between π/2 and π is the sine function, denoted as y = sin(x). To find this answer, you need to understand the properties of the sine function, specifically its amplitude and periodicity.
2. You are also correct! The trig function that never crosses the x-axis and has a value of 2 at π/6 is the cosine function, denoted as y = cos(x). To reach this answer, you need to know the properties of the cosine function, such as its periodicity and the values it takes at specific angles.
3. Your answer is incorrect. The trig function that has a period of π and is undefined for -π/2, π/2, 3π/2... is the cosecant function, denoted as y = csc(x). The cosecant function is the reciprocal of the sine function, which means it is undefined at the points where the sine function equals zero.
4. Your answer is incorrect. The trig function that has a period of 2π, is continuous, and is increasing for 0 < x < π/2 is the tangent function, denoted as y = tan(x). The tangent function is defined as the ratio of the sine function to the cosine function, and it has certain characteristics that make it suitable for this description.
In summary:
3. The correct answer is y = csc(x) for the given conditions.
4. The correct answer is y = tan(x) for the given conditions.