Basic Trigonometric Functions
This is the ratio of the opposite side to the hypotenuse in a right triangle.
What is sine?
The period of the sine and cosine functions.
What is 2pi?
The Pythagorean identity involving sine and cosine.
What is sin^2(x) + cos^2(x) = 1?
The principal value of sin^-1(1).
What is pi/2?
The height of a tree if the angle of elevation to the top is 30 degrees and the distance from the base is 10 meters.
What is 5 meters?
This function is defined as the ratio of the adjacent side to the hypotenuse.
What is cosine?
The amplitude of y = 3sin(x).
What is 3?
The identity for tan(x) in terms of sine and cosine.
What is tan(x) = (sin(x))/(cos(x))?
The range of cos^-1(x).
What is [0, pi]?
The length of the hypotenuse in a right triangle if one side is 3 and the other side is 4.
What is 5?
This trigonometric function is the ratio of the opposite side to the adjacent side.
What is tangent?
The horizontal shift in the function y= cos(x - pi).
What is pi units to the right?
The double-angle formula for cosine.
What is cos(2x) = cos^2(x) - sin^2(x)?
The principal value of tan^-1(0).
What is 0?
The area of a triangle with sides 7, 8, and an included angle of 60 degrees.
What is 14sqrt3?
The reciprocal of sine.
what is cosecant?
The vertical shift in the function y = sin(x) + 2.
What is 2 units up?
Simplify sin(x)cos(x) using a double-angle identity.
What is 1/2(sin(2x))?
Evaluate sin(sin^-1(1/2)).
What is 1/2?
The period of a Ferris wheel modeled by (h(t) = 10sin((pi/6)t)\).
What is 12?
The reciprocal of tangent.
What is cotangent?
The period of the tangent function.
What is pi?
Solve for x if cos(x) = 1/2 in the interval [0, 2pi].
What is x = pi/3, 5pi/3?
Solve cos^-1(x) = pi/4.
What is x = sqrt2/2?
Find the angle of elevation to the top of a 20-meter building from a point 15 meters away from the base.
What is tan^-1(4/3)?