Solutions Manual For Calculus Early Transcendental Functions
7th Edition By Ron Larson; Bruce H. Edwards 9781337552516
ALL Chapters
What angles do the definitions of trigonometric functions cover? - ANSWER: Any angle
If Θ is an acute angle, what do the definitions of its trigonometric functions coincide with? - ANSWER:
Those given in the preceding section.
To calculate the definition of trigonometric functions of any angle, what do you need? - ANSWER: Θ,
an angle in standard position with (x, y) a point on the terminal side of Θ
r - ANSWER: sq(x^2 + y^2) ≠ 0
sinΘ - ANSWER: y/r
cosΘ - ANSWER: x/r
What does cotΘ equal if y = 0? - ANSWER: Undefined
tanΘ - ANSWER: y/x, x ≠ 0
What does tanΘ equal if x = 0? - ANSWER: Undefined
cotΘ - ANSWER: x/y
secΘ - ANSWER: r/x, x ≠ 0
What does secΘ equal if x = 0? - ANSWER: Undefined
cscΘ - ANSWER: r/y, y ≠ 0
What does cscΘ equal if y = 0? - ANSWER: Undefined
Because r = sq(x^2 + y^2) cannot equal zero, what follows? - ANSWER: The sine and cosine functions
are defined for any real value of Θ.
If x = 0, what trigonometric functions are undefined? - ANSWER: Tangent (tan) and secant (sec)
If y = 0, what trigonometric functions are undefined? - ANSWER: Cotangent (cot) and cosecant (csc)
(EXAMPLE 1) If you have a point with known x and y values on the terminal side of angle Θ, how do
you find the sine, cosine, and tangent of Θ? - ANSWER: - Use the values of x and y to find r.
- Then, calculate the trigonometric functions according to their definitions
How can the signs of the trigonometric functions in the four quadrants be determined? - ANSWER:
From the definitions of the functions
In quadrant I, what are the values of x and y? - ANSWER: x > 0; y > 0
In quadrant II, what are the values of x and y? - ANSWER: x < 0; y > 0
In quadrant III, what are the values of x and y? - ANSWER: x < 0; y < 0
7th Edition By Ron Larson; Bruce H. Edwards 9781337552516
ALL Chapters
What angles do the definitions of trigonometric functions cover? - ANSWER: Any angle
If Θ is an acute angle, what do the definitions of its trigonometric functions coincide with? - ANSWER:
Those given in the preceding section.
To calculate the definition of trigonometric functions of any angle, what do you need? - ANSWER: Θ,
an angle in standard position with (x, y) a point on the terminal side of Θ
r - ANSWER: sq(x^2 + y^2) ≠ 0
sinΘ - ANSWER: y/r
cosΘ - ANSWER: x/r
What does cotΘ equal if y = 0? - ANSWER: Undefined
tanΘ - ANSWER: y/x, x ≠ 0
What does tanΘ equal if x = 0? - ANSWER: Undefined
cotΘ - ANSWER: x/y
secΘ - ANSWER: r/x, x ≠ 0
What does secΘ equal if x = 0? - ANSWER: Undefined
cscΘ - ANSWER: r/y, y ≠ 0
What does cscΘ equal if y = 0? - ANSWER: Undefined
Because r = sq(x^2 + y^2) cannot equal zero, what follows? - ANSWER: The sine and cosine functions
are defined for any real value of Θ.
If x = 0, what trigonometric functions are undefined? - ANSWER: Tangent (tan) and secant (sec)
If y = 0, what trigonometric functions are undefined? - ANSWER: Cotangent (cot) and cosecant (csc)
(EXAMPLE 1) If you have a point with known x and y values on the terminal side of angle Θ, how do
you find the sine, cosine, and tangent of Θ? - ANSWER: - Use the values of x and y to find r.
- Then, calculate the trigonometric functions according to their definitions
How can the signs of the trigonometric functions in the four quadrants be determined? - ANSWER:
From the definitions of the functions
In quadrant I, what are the values of x and y? - ANSWER: x > 0; y > 0
In quadrant II, what are the values of x and y? - ANSWER: x < 0; y > 0
In quadrant III, what are the values of x and y? - ANSWER: x < 0; y < 0
