Trigonometry: Chapter 6
What are the signs for π < θ < 3π/2 or quadrant III?
(-x,-y)
What are the signs for π/2 < θ < π or quadrant II?
(-x,y)
Find the value of sin(45°) + cos (60°)
(1+√2)/2
What are the signs for 3π/2 < θ < 0 or quadrant IV?
(x,-y)
What are the signs for 0 < θ < π/2 or quadrant I?
(x,y)
Find the exact value of sin(11π/2)
-1
Convert -5π/2 to degrees
-450
cot(-θ) =
-cot(θ)
csc(-θ) =
-csc(θ)
sin(-θ) =
-sin(θ)
tan(-θ) =
-tan(θ)
2 sin(π/3) - 3 tan(π/6)
0
sin²x + cos² x=?
1
Convert 1°2'3" to degrees, round to 4 decimal places
1.0342
How do you find sec on a calculator?
1/cos(x)
How do you find cot on a calculator?
1/cot(x)
How do you find csc(x) on a calculator?
1/sin(x)
Convert 18.255° to time
18°15'18"
The period of sin, cos, csc, sec
2π
(√3/2, 1/2)
30 degrees
Convert 135° to radians, write in terms of pi
3π/4
(√2/2, √2/2)
45 degrees
(1/2, √3/2)
60 degrees
What does the "A" of y = A sin(ω(x-Φ/ω)) + B mean?
Amplitude
ω = θ/t
Angular Speed
s=θr
Arc length
A=1/2(r²θ)
Area of a Sector
Domain and range of cos
D: (-∞,∞) R: [-1,1]
Domain and range of sin
D: (-∞,∞) R: [-1,1]
Domain and range of csc
D: {x | x≠ multiples of 180° or π} R:(-∞,-1] U [1,∞)
Domain and range of tan
D: {x | x≠ odd multiples of 90° or π/2} R: (-∞,∞)
Domain and range of sec
D: {x | x≠ odd multiples of 90° or π/2} R:(-∞,-1] U [1,∞)
Domain and range of cot
D:{x | x≠ multiples of 180° or π} R:(-∞,∞)
If given X.YZ° use: X° YZ(60)' You should get: Y.Z use X° Y' Z(60)"
Degrees to Time
x° ⋅ π/180
Degrees to radians
What does the "ω" of y = A sin(ω(x-Φ/ω)) + B do?
Determines the period
1. Coordinate 1 minus Coordinate 2 2. If the coordinate is in minutes it is converted to radians 3. Use the arc length formula to find the distance
Finding distance between Coordinates
1. Find the coordinate for the given radian or degree 2. Plug the coordinate into the formula
Finding exact value
When do you use the trig functions of radius?
For coordinates not on the unit circle
x² + y² = r², used with coordinates on a circle
Formula for radius
(0,0),(π/2, 1), (π,0), (3π/2, -1), (2π,0)
Key Points of Sin
(-π/4, -1), (0,0), (π/4, 1)
Key Points of Tan
(0,1), (π/2, 0), (π,-1), (3π/2, 0), (2π,1)
Key points of Cos
(π/4, 1), (π/2), (3π/4, -1)
Key points of Cot
(-3π/2, 1), (-π/2, -1). (π/2, 1), (3π/2, -1)
Key points of csc
(-2π, 1), (-π, -1), (0,1), (π,-1), (2π, 1)
Key points of sec
V = s/t V = rω
Linear Speed
What does the "Φ/ω" of y = A sin(ω(x-Φ/ω)) + B do?
Phase shift (Horizontal shift)
x ⋅ 180/π
Radians to degrees
If given X°Y'Z" use: X° + Y/60 + Z/3600
Time to Degrees
What does the "B" of y = A sin(ω(x-Φ/ω)) + B do?
Vertical shift
...-π/2, π/2, 3π/2...
asymptotes of tan and sec
...0, π, 2π...
asymtotes of cot and csc
cos(-θ) =
cos(θ)
What is the trigonometric function for cosine?
cos=X
What is the cos function of using radius?
cos=x/r
What is the cot function of using radius?
cot=x/y
What is the trigonometric function for cotangent?
cot=x/y
What is the trigonometric function for cosecant?
csc=1/y
What is the csc function of using radius?
csc=r/y
cot²x +1
csc²x
cos, sec are (odd/even)
even
Sin, tan, csc, cot are (odd/even)
odd
sec(-θ) =
sec(θ)
What is the trigonometric function for secant?
sec=1/x
What is the sec function of using radius?
sec=r/x
tan²x + 1 =?
sec²x
What are the six trig functions for (√3/2, 1/2)?
sin=1/2, cos=√3/2, tan=√3/3, csc=2, sec=2√3/3, cot=√3
Find the trig functions of (-3,4)
sin=4/5, cos=-3/5, tan=-4/3, csc=5/4, sec=-5/3, cot=-3/4
What is the trigonometric function for sine?
sin=Y
What is the sin function of using radius?
sin=y/r
What is the tan function of using radius?
tan=y/x
What is the trigonometric function for tangent?
tan=y/x
The period of tan, cot
π