Relating to The Unit Circle
1) An angle of measure 13π/12 when converted into degrees.
2) An angle of measure 18 degrees when converted into radians.
1) What is 195 degrees?
2) What is π/10?
The arc length of a section of a circle with an angle of 45 degrees and a radius of 12 inches.
What is 3π inches?
The six trigonometric functions, as they relate to sides of a right triangle.
What is sine = opposite / hypotenuse, cosine = adjacent / hypotenuse,
tangent = opposite / adjacent, cosecant = hypotenuse / opposite,
secant = hypotenuse / adjacent and cotangent = adjacent / opposite?
The exact value of arcsin(√(3)/2).
What is π/3 radians?
1) The smallest positive and negative coterminal angles of 45 degrees.
2) The smallest positive and negative coterminal angles of 120 degrees.
1) What is 405 degrees / -315 degrees?
2) What is 480 degrees / -240?
The radius of a circle whose arclength measure 5 meters with an angle of 60 degrees.
What is 12.5/π meters?
The exact value of the following three expressions.
1) tan(150° )
2) sec(7π/4)
3) csc(-π)
1) -√(3)/3
2) √2
3) Undefined
All key characteristics of function f(x)=3cos(1/3x−5π/6)-1.
What is an amplitude of 3, period of 6π, phase shift of 5π/2 right, and midline equation of y = -1?
1) The range of the arcsin function.
2) The range of the arccos function.
3) The range of the arctan function.
1) What is [-π/2, π/2]?
2) What is [0, π]?
3) What is [-π/2, π/2]?
When converted from degrees, minutes and seconds into radians, the angle is π/7.
What is 25 degrees, 42 minutes, and ~51.43 seconds?
The area of a slice of pizza (1/6th the size of the whole pizza) when the diameter of the pizza is 16 inches.
What is 32π in^2?
The exact value of sin(x), given that cos(x) is (3/5) and tan(x) < 0.
What is -4/5.
arccos(sin(17π/6)), evaluated in radians.
What is 2π/3?
1) The reference angle to 213 degrees.
2) The reference angle to 11π/7.
1) What is 33 degrees?
2) What is 3π/7?
The angular speed (in rad/sec) of a rolling ball with radius of 1/3rd feet when it is traveling at 15 miles per hour.
What is 66 radians per second?
Two Pythagorean identities connecting the outputs of the non-sinusoidal trigonometric functions, derived from the identity (sin(x))^2 + (cos(x))^2 = 1.
What are 1 + (tan(x))^2 = (sec(x))^2 and 1 + (cot(x))^2 = (csc(x))^2?
The amplitude, period, midline, and phase shift of the following sine function.
https://imgur.com/a/5ezmML9
What is an amplitude of 2, midline equation of y = -4, period of 2, and equation of f(x) = 2sin(πx) - 4?
tan(arcsin(x+3)), for -4<x<-2.
What is (x-3)/(√(-x^2+6x-8))?
1) The measure of angle A if tan(A) = 1, and sin(A) is negative.
2) Cos(B) if sin(B)=1/2 and tan(B) is negative.
1) What is 225 degrees?
2) What is -√(3)/2?
The linear (mph) speed of a point on a wheel with diameter of 18 inches when the time it takes for the wheel to make one revolution is .5 seconds.
What is 6.43 miles/hour?
The height of a building when the angle of elevation is found to be 9 degrees from the ground, and the horizontal distance to the building is found to be 2000 feet.
What is ~316.77 feet?
A sketch of the basic tangent, cotangent, secant, and cosecant non-translated graphs.
What is:
The angle the road makes with the horizontal in radians when the grade of a road is 7%. (This means that for every horizontal distance of 100 feet on the road, the vertical rise is 7 feet.)
What is arctan(7/100) = ~0.06988 radians = ~4.004 degrees?