Trigonometry: Chapter 6

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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

(√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


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