Calculus -- Sec 4.4_ Trigonometric Functions of Any Angle exam with complete solutions.
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Course
Math
Institution
Math
What angles do the definitions of trigonometric functions cover?
Any angle
If Θ is an acute angle, what do the definitions of its trigonometric functions coincide with?
Those given in the preceding section.
To calculate the definition of trigonometric functions of any angle, what d...
Calculus -- Sec 4.4: Trigonometric
Functions of Any Angle exam with
complete solutions
hat 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
In quadrant IV, what are the values of x and y? - ANSWER-x > 0; y < 0
In quadrant I, what does Θ equal? - ANSWER-0 < Θ < π/2
In quadrant II, what does Θ equal? - ANSWER-π/2 < Θ < π
In quadrant III, what does Θ equal? - ANSWER-π < 3π/2
In quadrant IV, what does Θ equal? - ANSWER-3π/2 < Θ < 2π
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