Chapter 4 (4.1 to 4.7) Flashcards by Jessica Brooks

What are co-terminal angles and how do you find them?

Two or more different angles with the same initial and terminal rays

+/- 360*
+/- 2pie

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What are the two ways you can write an angle in degrees?

Decimal 25.5*

Degrees, minutes, seconds 25*30’0”

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What is 360* in radians?

2 pie

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What is 180* in radians?

Pie

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What is 90* in radians?

Pie/2

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What is 45* in radians?

Pie/4

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What is 30* in radians?

Pie/6

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What is 60* in radians?

Pie/3

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What are the four quadrants and what is it called when it is on an axis?

1-4 counter clockwise

Quadrantal

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What are complementary angles?

2 angles that add to 90*or pie/2

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What are supplementary angles?

2 angles that add to 180* or pie

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How do you convert between degrees and radians?

D->R multiply by pie/180*

R->D multiply by 180*/pie

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What are the three ways to find the area of a sector? (Angle in D and R, arc length)

(A is area)

A = theta/360* times pie times radius^2 (degrees)
A = theta times 1/2 times radius^2 (radians)
A = 1/2 times radius times arc length

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What are the two ways to find arc length? (D and R)

(S is arc length)
S = theta times radius (radians)
S = theta/360* times 2pie times radius (degrees)

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What is the unit circle?

A circle centered at the origin with a radius of 1

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How do you find the six trig functions withs unit circle?

Cos theta is x
Sec theta is 1/x
Sin theta is y
Csc theta is 1/y
Tan theta is y/x
Cot theta is x/y

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What are the unit circle coordinates for 30, 45, and 60*, and where do you measure from?

30* or pie/6: (square root of 3 over 2, 1/2)
45* or pie/4: (square root of 2 over 2, “”)
60* or pie/3: (1/2, square root of 3 over 2)

X-axis

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What are the six trig functions of a right triangle?

Sin= opp/hyp
Csc= hyp/opp
Cos= adj/hyp
Sec= hyp/adj
Tan= opp/adj
Cot= adj/opp

Soh-cah-toa

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When sketching angles, what are the three things you need and what direction do you go?

Study These Flashcards

Two rays, one starting on the positive x-axis and a theta sign

Positive is counter-clockwise
Negative is clockwise

What is Sin(90* - theta)?

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Cos theta

What is Cos(90* - theta)?

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Sin theta

What is Tan(90* - theta)?

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Cot theta

What is Cot(90* - theta)?

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Tan theta

What is Sec(90* - theta)?

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Csc theta

What is Csc(90* - theta)?

Sec theta

What are the six reciprocal identies?

``` Cos theta=1/sec theta Sec theta=1/cos theta Sin theta=1/csc theta Csc theta=1/sin theta Tan theta=1/cot theta Cot theta=1/tan theta ```

What are the two quotient identies?

Tan theta = sin theta/cos theta | Cot theta = cos theta/sin theta

What are the three pythagorean identies?

Cos^2 theta + sin^2 theta = 1 1 + tan^2 theta = sec^2 theta Cot^2 theta + 1 = csc^2 theta

How do you find the six trig functions with a circle that has a radius other than 1?

Cos theta: x/r, Sec theta: r/x, Sin theta: y/r, Csc theta: r/y, Tan theta: y/x, Cot theta: x/y

What is the sentence to remember where the three trig functions are positive?

All Students Take Calculus, all functions are + in Quad 1, only sin in 2, only tan in 3, only cos in 4

What is the reference angle?

The positive acute angle formed by the terminal side of theta and the x-axis. It is called theta'

What does the graph of sin look like? (Unit circle, with fundamental period and domain and range)

At the origin, up at one at pie/2, 0 at pie, -1 at 3pie/2, zero at 2pie F.P is 2pie, D (-infinity, infinity), R [-1,1]

What does the graph of cos look like? (Unit circle, with fundamental period and domain and range)

Up at one at the origin, zero at pie/2, -1 at pie, zero at 3pie/2, one at 2pie F.P is 2pie, D (-infinity, infinity), R [-1,1]

For Y=a*cos*b*x and Y=a*sin*b*x, how do you find the amplitude and fundamental period and what does the graph look like when a is negative?

Amplitude is |a|, fundamental period is 2pie/b, upside down

When the sin/cos graphs are Y=a*cos*b*x-c or Y=a*sin*b*x-c how do they change and how do you know how to change them?

They shift horizontally, new left and right endpoints are found with bx-c=0 and bx-c=2pie (solve for x)

When the sin/cos graphs are Y=a*cos*b*x-c + d or Y=a*sin*b*x-c + d how do they change and how do you know how to change them?

They move vertically d units up

What does the graph of tan look like? (Unit circle, with fundamental period and domain and range)

At the origin, at one at pie/4, approaching the asymptote of pie over two, negative one at -pie/4 approaching the asymptote of -pie/2 F.P is pie, D (theta not = pie/2 + pie*n, n e z), R (-infinity, infinity)

What does the graph of cot look like? (Unit circle, with fundamental period and domain and range)

Asymptote of 0 and pie, on the x-axis at pie/2, up at one at pie/4 and down to -1 at 3pie/4 F.P is pie, D (theta not = 0 + pie*n, n e z), R (-infinity, infinity)

For Y=a*tan*b*x and Y=a*tan*b*x, how do you find the height midway to the asymptote and fundamental period and what does the graph look like when a is negative?

A= + height midway to asymptote, F.P is pie/b, flipped (like negative slope)

When the tan/cot graphs are Y=a*tan*b*x-c or Y=a*cot*b*x-c how do they change and how do you know how to change them?

They shift horizontally, new left and right endpoints for tan are found with bx-c=-pie/2 and bx-c=pie/2 (solve for x); new left and right endpoints for cot are found with bx-c=0 and bx-c=pie (solve for x)

What is the period, domain, and range of Y=sec(x) and Y=csc(x), and what do they look like?

Sec- period is 2pie, domain is theta not equal to pie/2 plus pie*n (n E Z), range is (-infinity, -1] U [1, infinity) Csc- period is 2pie, domain is theta not equal to pie*n (n E Z) range is (-infinity, -1] U [1, infinity) They have asymptotes where cos (for sec) and sin (for csc) hit the x-axis and are u shaped going away from the slope of cos or sin

Where is the graph of arcsin restricted?

Quads 1 and 4

Where is the graph of arccos restricted?

Quads 1 and 2

Where is the graph of arctan restricted?

Quads 1 and 4

What is tan(30*)?

Square root of 3/3

What is tan(45*)?

What is tan(60*)?

square root of 3

Chapter 4 (4.1 to 4.7) Flashcards

(47 cards)