6.2 Inverse Trigonometric Funtions
Objective: Find the exact value of expressions involving inverse trig functions Complex tangent function f ( z ) = tan z. Corners at ± π ± π i
Title: Feb 5­3:48 PM (1 of 7)
y = csc­1x for x < ­1 and x > 1 and ­π/2 < y < π/2 y ≠ 0 y = sec­1x for x < ­1 and x > 1 and 0 < y < π y = cot­1x Cosecant
Same as the Sine!!!
for ­∞ < x < ∞ and 0 < y < π Secant
Same as the Cosine!!!
Sent graphs to the back
Title: Feb 5­3:48 PM (2 of 7)
y ≠ π/2
Cotangent
Angle values
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Sin
Csc
Cos
for ­1 x 1 for x for ­ x and ­ /2 y /2
and ­ y and 0 y Sec
Tangent
Csc y = 0
Sec y = /2
Cot
Title: Feb 5­3:48 PM (3 of 7)
Find Exact Values
sin­1(sin(5π/4)) ⇒ start on the inside...
sin(5π/4) = ­√2/2
= sin­1(­√2/2) = ­ π/4 because this is in our interval
sin(tan­1(1/2)) = start by making a triangle
fill in the information the tangent gave us &
5
1
find the third side of the triangle
2
We don't care what the value of θ is.
= to find sin (θ) we look at the triangle
= 1/√5 = √5/5
Title: Feb 5­3:48 PM (4 of 7)
csc(cot­1(7/6)) = start by making a triangle
fill in the information the cotangent √62 + 72 =√36 + 49 =√85
gave us & find the third side of the triangle
√85
6
7
= to find csc (θ) we look at the triangle
= √85
/6 sec(sin­1(­5/13)) = start by making a triangle
fill in the information the sine gave us &
find the third side of the triangle
(­5)2 + x2 = 132 25 + x2 = 169
x 2 = 144
x = 12
= to find sec (θ) we look at the triangle
= 13/12 Title: Feb 5­3:48 PM (5 of 7)
13
5
12
Homework:
page 464
(9 - 36)
Title: Feb 5­3:48 PM (6 of 7)
Title: Feb 5­3:48 PM (7 of 7)