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Notes March 8
Chapter 6-4
Objective:
Inverse Trig Functions
Name_____________
Be able to evaluate inverse trigonometric functions
Lesson:
Inverse functions interchange the coordinates of the ordered pairs of the
function so the domain, x, becomes the range, y, and the range, y becomes the domain, x.
Comparison Table:
sin(x)
Graph:
sin-1(x) or arcsin(x)
Graph:
Domain ____________
Domain __________
Range________
Range __________
(____, ____)
(____,_____)
(____, ____)
(____, ____)
__________
__________ (failed vertical line test)
Sin(x) = __________
x = __________
Sin(x) is the value of sine of an angle x is .3393
x is all the ______ whose sine is .3393
The Inverse Functions are written:
Ex.
sin(x) = y
A = cos(b)
tan(θ) = z
__________ or __________
__________ or __________
__________ or __________
Ex. Find all positive values of x for which cosx = ½ (look on your unit circle)
x = cos-1 (1/2) so x = __________ and __________
so between 0 and 360, we have: ______ and ______
Find all positive values of x for which sin x = (1/√2) between 0 and 360
sinx = √2/2
Ex. Evaluate each expression. Assume that all angles are in quad 1
cos(arccos (1/2) =
cos(arccsc(5/3)) =
Notes March 8
Chapter 6-4
Inverse Trig Functions
sec(arctan (7/13)) =
sin(arcsin(13/14) =
cot(tan(5/10) =
Ex. Verify each equation.
arccos √3/2 + arcsin √3/2 = arctan 1 + arccot 1
tan-1 ¾ + tan-1 5/12 = tan-1 56/33
put in calculator
arcsin 3/5 + arcos 15/17 = arctan77/36
put in calculator
Homework: pg. 331 16 – 44 even
Name_____________
Notes March 8
Chapter 6-4
Inverse Trig Functions
Name_____________
What I will be doing and the student will be filling in
Lesson Plan #21
Inverse Trig Functions
Chapter 6-4
Objective:
Be able to evaluate inverse trigonometric functions
Introduction: Remember when you talked about inverse functions before? For instance if y =
2x+3, then the inverse of y = (x-3)/2. Or for y = x2 the inverse was y = √𝑥? It’s like putting on
your socks before shoes, and the inverse is taking of the shoes first and then the socks. We
have already briefly discussed inverses of trig functions, with arc-sine, arc-cosine, and arctangent. These are different than cosecant, secant, and cotangent because the inverse
functions are not really functions because they have multiple y values for the same x values.
Lesson:
Recall inverse functions interchange the coordinates of the ordered pairs of the function
so the domain becomes the range and the range becomes the domain.
Do Table:
Sin(x)
Domain (all reals)
Range(-1<y<1)
(x, sin(x))
(90, 1)
Function
sin-1(x) or arcsin(x)
Domain (-1<y<1)
Range (all reals)
(sin(x), x)
(1, 90)
not a function (failed vertical line
Sin(x) = (0.3393)
The value of sine of an angle x is .3393
x = sin-1(x) or arcsin(x)
cos-1 (A) = b
tan-1 z = θ
x = sin-1(0.3393)
x is all the angles whose sine is .3393
test)
Sin(x) = y
A = cos(b)
Tan(θ) = z
Show pictures
ex. Find all positive values of x for which cosx = ½ look on your unit circle
x = cos-1 (1/2) so x = 60, 300, 420….. and π/3, 5 π/3, 7 π/3……
so between 0 and 360, we have 60 and 300
Find all positive values of x for which sin x = (1/√2) between 0 and 360
Notes March 8
Chapter 6-4
Inverse Trig Functions
Sinx = √2/2 so 45, 135
Ex. Evaluate each expression. Assume that all angles are in quad 1
cos(arccos (1/2) = ½
cos(arccsc(5/3)) = 4/5
sec(arctan (7/13)) = √365/7
On their own: sin(arcsin(13/14) = 13/14
cot(tan(5/10) = 10/5
Ex. Verify each equation.
arccos √3/2 + arcsin √3/2 = arctan 1 + arccot 1
30 + 60 = 45 +45
-1
tan ¾ + tan-1 5/12 = tan-1 56/33
put in calculator
36.9 + 22.6 = 59.5
arcsin 3/5 + arcos 15/17 = arctan77/36
put in calculator
36.9 + 28.1 = 65
Homework: pg. 331 16 – 44 evens
Name_____________