30 Questions
What is the range of the sine and cosine functions?
[-1, 1]
How can you evaluate trigonometric functions for nonacute angles?
Using reference angles and reference right triangles
What is the formula for the tangent function in terms of x and y?
y/x (x ≠ 0)
What is the significance of the point (x, y) in defining trigonometric functions?
It is a point on the terminal side of an angle θ in standard position
What is the relationship between the values of the sine and cosecant functions?
They are reciprocals of each other
In which quadrants can the terminal side of an angle θ lie if tan θ is positive and cos θ is negative?
II or III
What is the maximum value of the sine function?
1
What is the relationship between the sine and cosecant functions?
csc(u) = 1/sin(u)
In what quadrant would the terminal side of the angle lie if the cosine value is negative and the sine value is positive?
II
What is the range of the secant function?
All real numbers except -1 and 1
What is the period of the sine function?
360°
What is the relationship between the tangent and cotangent functions?
tan(u) = 1/cot(u)
What is the exact value of $u$ that satisfies the equation $sin(u) = 2$ in the interval $0 ≤ u ≤ 2π$?
There is no solution in the interval $0 ≤ u ≤ 2π$ because $sin(u) ≤ 1$ for all values of $u$.
Find the exact values of $u$ that satisfy the equation $cos(u) = -1/3$ in the interval $0 ≤ u ≤ 2π$.
The exact values of $u$ are $u = π + arcsin(1/3) ≈ 2.288$ and $u = 2π - arcsin(1/3) ≈ 3.852$.
What is the expected temperature on February 15 in Peoria, Illinois, according to the formula $T = 50 - 28 cos(2π(x - 31)/365)$?
The expected temperature is $T = 50 - 28 cos(2π(46 - 31)/365) ≈ 24.4°F$.
Find the exact values of $u$ that satisfy the equation $tan(u) = 3$ in the interval $0 ≤ u ≤ 2π$.
The exact values of $u$ are $u = arctan(3) ≈ 1.249$ and $u = π + arctan(3) ≈ 4.391$.
What is the expected temperature on August 15 in Peoria, Illinois, according to the formula $T = 50 - 28 cos(2π(x - 31)/365)$?
The expected temperature is $T = 50 - 28 cos(2π(228 - 31)/365) ≈ 73.4°F$.
Find the exact values of $u$ that satisfy the equation $csc(u) = 2$ in the interval $0 ≤ u ≤ 2π$.
The exact values of $u$ are $u = π/6$ and $u = 5π/6$.
If sin u is positive and cos u is negative, in which quadrant does the terminal side of u lie?
Quadrant II
If tan u is negative and sec u is positive, in which quadrant does the terminal side of u lie?
Quadrant IV
If cot u is positive and csc u is negative, in which quadrant does the terminal side of u lie?
Quadrant I
If sin u = -a/b and the terminal side of u lies in Quadrant III, what is the value of cos u?
-√(1 - (a/b)^2)
If tan u = a/b and the terminal side of u lies in Quadrant II, what is the value of sin u?
-b/√(a^2 + b^2)
If sec u = -a/b and the terminal side of u lies in Quadrant III, what is the value of tan u?
b/√(a^2 - b^2)
If the terminal side of an angle $u$ lies in Quadrant IV, what is the sign of its sine and cosine?
The sine is negative, and the cosine is positive.
What is the relationship between the sine and cosine of an angle in Quadrant III and the same angle in Quadrant IV?
They are the same, but with opposite signs.
How can you find the exact values of trigonometric functions using the unit circle?
By using the coordinates of the terminal side of the angle on the unit circle.
If $
m{\sin} u = -0.3420$, and the terminal side of $u$ lies in Quadrant IV, what is the value of $
m{\cos} u$?
approximately 0.9397
What is the difference between the trigonometric functions of an angle in Quadrant III and the same angle in Quadrant IV?
The signs are opposite.
How can you use the fact that sine is an odd function and cosine is an even function to find the exact values of trigonometric functions?
By using the properties of odd and even functions, such as $
m{\sin}(-x) = -
m{\sin}(x)$ and $
m{\cos}(-x) =
m{\cos}(x)$.
Learn about trigonometric functions, their ranges, and how to evaluate them for non-acute angles using reference angles and triangles. This quiz covers Section 4.3 of Trigonometry Chapter 4.
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