Download Section P.6: Trigonometry 1. Degrees and radians What is a radian

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
page
11
page
12
page
13
page
14
page
15
Document related concepts
no text concepts found
Transcript 
Section P.6: Trigonometry
1. Degrees and radians
What is a radian?
How many radians in a circle?
How do we convert between degrees and radians?
October 06, 2015
October 06, 2015
2. Values of trig functions
a. definitions:
sine
cosecant
cosine
secant
tangent
cotangent
3. Special Right Triangles
45º
30º
45º
60º
angle 0
sine
cosine
π/6
π/4
π/3
π/2
October 06, 2015
4. Values of trig functions
sin (π/2)
tan(3π / 4)
sec(2π / 3)
cot(-π /2)
cos (7π/6)
csc(-3π/4)
sec(7π/3)
tan(17π/6)
October 06, 2015
Example 1: If cos θ = 2/3 and sin θ < 0, find the values of all 6
trig functions.
Example 2: If sin θ = x/2 and π/2 < x < π, find the values of all 6
trig functions.
October 06, 2015
5. Inverse Trig Functions
written as arcsinx or sin-1x
An inverse trig function finds the _________ whose sine (cosine,
tangent, etc.) is given.
Domain restrictions:
sin and tan
Examples: Find...
arcsin(√(3) / 2)
cos
arccsc(-2)
sin(arctan(1))
cos(arcsin(-3/5)
sin(arctanx)
cos(arcsinx)
October 06, 2015
6. Solving trig equations
a.first method: isolate the trig function, and then find all
angles (usually 2) that have those trig values.
examples: 2sinx - 1 = 0
3tan2 x - 1 = 0
6. Solving trig equations (continued)
b.second method: factor out trig functions
examples: 2sinxcosx = sinx
sec2 x + 2secx = 0
October 06, 2015
6. Solving trig equations (continued)
c. last method: use a trig identity to substitute, such as the...
Pythagorean identities:
examples: sin2x - cosx + 1 = 0
3sinx - 2cos2x = -3
October 06, 2015
October 06, 2015
7. Sinusoids
general equation:y = Asin(B(x - C)) + D or
y = Acos(B(x - C)) + D
A=
B=
C=
D=
sine graph
cosine graph
October 06, 2015
Example 1: Graph y = 2sin((π/2)(x - 3))
Example 2: Graph y = -3cos(2x) + 1
Example 3: Find an equation for the sinusoid shown below
Example 4: Find an equation for the sinusoid shown below
October 06, 2015
Section P.6
1. a. 0
b.-√2 / 2
d. undef.
e. -2
3. cosB =
tanB =
secB =
=
2. a. π/3
c. √(1 - 4x2)
4. a.
b.
c.
d.
e.
f.
c. -√3
-5√21
21
=
2√21
cscB =
21
cotB =
b. π/3
d.
1
or √(1 + x2)
√(1 + x2)
1 + x2
π/6, 11π/6
π/4, 3π/4 ,5π/4, 7π/4
π/2, 3π/2
π/3, 2π/3, 4π/3, 5π/3
π/2, 3π/2, π/6, 11π/6
π/3, 5π/3
5. x = .7227, π
f. 1
October 06, 2015
October 06, 2015
October 06, 2015
October 06, 2015
Related documents