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Questions and Answers
Given tan x + cotx = $\frac{1}{\sqrt{3}}$, then find sin 2x
Given tan x + cotx = $\frac{1}{\sqrt{3}}$, then find sin 2x
$\frac{\sqrt{3}}{2}$
If tan a = $\frac{1}{2\sqrt{2}}$, where $\pi$ < a < $\frac{3\pi}{2}$. Find the value of cos 2a.
If tan a = $\frac{1}{2\sqrt{2}}$, where $\pi$ < a < $\frac{3\pi}{2}$. Find the value of cos 2a.
$\frac{-7}{9}$
Evaluate $\frac{\sin 30° \cos 30°}{\sin 13° \cos 13°}$
Evaluate $\frac{\sin 30° \cos 30°}{\sin 13° \cos 13°}$
$\frac{\sqrt{3}}{2}$
Solve the equation sin x = $\frac{\sqrt{2}}{2}$ for x ∈ [0,2π].
Solve the equation sin x = $\frac{\sqrt{2}}{2}$ for x ∈ [0,2π].
Find the general solution of the following trigonometric equations.
a) cos(7x) = $\frac{1}{2}$
Find the general solution of the following trigonometric equations. a) cos(7x) = $\frac{1}{2}$
Find the general solution of the following trigonometric equations. b) tan (x - $\frac{\pi}{4}$) = $\frac{-1}{\sqrt{3}}$
Find the general solution of the following trigonometric equations. b) tan (x - $\frac{\pi}{4}$) = $\frac{-1}{\sqrt{3}}$
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND.
a) f(-6)
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND. a) f(-6)
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND.
b) lim f(x)
x→-1-
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND.
b) lim f(x)
x→-1-
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND.
e) Write discontinuity points of the function f(x) on the interval (-9,9).
Evaluate the following limits by using the graph of the function f(x) shown below. If the limit does not exist, write DNE. If the value of the function f(x) is undefined, write UND.
e) Write discontinuity points of the function f(x) on the interval (-9,9).
Evaluate the following limits
a) lim $\frac{-x^2 + 1}{x-1-x^2+x+2}$
x→1-
Evaluate the following limits
a) lim $\frac{-x^2 + 1}{x-1-x^2+x+2}$
x→1-
Evaluate the following limits
b) lim $\frac{|2x-3|}{x-\frac{3}{2}}$
x→($\frac{3}{2}$)+
Evaluate the following limits
b) lim $\frac{|2x-3|}{x-\frac{3}{2}}$
x→($\frac{3}{2}$)+
The function f(x) is continuous for all x ∈ R? Find the values of a and b.
f(x) = {$\begin{matrix} \frac{x^2 +4}{3} & , if x<-2 \ -2 & , if x=-2 \ bx-1 & , if x>-2 \end{matrix}$
The function f(x) is continuous for all x ∈ R? Find the values of a and b. f(x) = {$\begin{matrix} \frac{x^2 +4}{3} & , if x<-2 \ -2 & , if x=-2 \ bx-1 & , if x>-2 \end{matrix}$
Find all values of k that would make the function f(x) continuous at x = -9. Justify your result.
f(x) = {$\begin{matrix} \frac{x^2+7x-18}{x^2 + 8x-9} & , for x≠-9 \ k & , for x = -9 \end{matrix}$
Find all values of k that would make the function f(x) continuous at x = -9. Justify your result. f(x) = {$\begin{matrix} \frac{x^2+7x-18}{x^2 + 8x-9} & , for x≠-9 \ k & , for x = -9 \end{matrix}$
Flashcards
tan x + cot x = 4/3
tan x + cot x = 4/3
The tangent of an angle added to the cotangent of the same angle equals 4/3.
Find sin 2x
Find sin 2x
Find the value of sin 2x.
tan α = 1/2, π < α < 3π/2
tan α = 1/2, π < α < 3π/2
The tangent of an angle is 1/2, with the angle in the range of pi to 3pi/2.
Find cos 2α
Find cos 2α
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Evaluate (sin 39° + cos 39°) / (sin 13° - cos 13°)
Evaluate (sin 39° + cos 39°) / (sin 13° - cos 13°)
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Solve sin x = -√2 / 2, x ∈ [0, 2π]
Solve sin x = -√2 / 2, x ∈ [0, 2π]
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Solve cos(7x) = 1/2
Solve cos(7x) = 1/2
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Solve tan(x - π/4) = -1/3
Solve tan(x - π/4) = -1/3
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Analyze f(x) from its graph
Analyze f(x) from its graph
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f(-6)
f(-6)
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lim f(x) as x→-1
lim f(x) as x→-1
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lim f(x) as x→6+
lim f(x) as x→6+
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lim f(x) as x→-6
lim f(x) as x→-6
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Discontinuities of f(x) on (-9,9)
Discontinuities of f(x) on (-9,9)
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lim (-x² + 1) / (-x² + x + 2) as x→-1
lim (-x² + 1) / (-x² + x + 2) as x→-1
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lim |2x - 3| / (x - 3/2) as x→(3/2)-
lim |2x - 3| / (x - 3/2) as x→(3/2)-
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Continuity of f(x)
Continuity of f(x)
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Find the value of a
Find the value of a
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Find the value of b
Find the value of b
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Continuity of f(x) at x = -9
Continuity of f(x) at x = -9
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Find the value of k
Find the value of k
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What is the tangent of an angle?
What is the tangent of an angle?
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What is the cotangent of an angle?
What is the cotangent of an angle?
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What is the double angle formula for sine?
What is the double angle formula for sine?
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What is the double angle formula for cosine?
What is the double angle formula for cosine?
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Study Notes
Exam Instructions and Information
- Exam duration: 40 minutes
- Show all work and clearly indicate the method used
- Accuracy of the final answer and the method are both graded
- Answers must include correct units if needed
- Write clearly and legibly
Exam Questions and Topics
- Question 1: Given tan x + cot x = √3, find sin 2x. (10 points)
- Question 2: If tan α = 1 / 2√2, where π < α < 3π/2, find cos 2α. (10 points)
- Question 3: Evaluate sin 39° / sin 13° * cos 39° / cos 13°. (10 points)
- Question 4: Solve the equation sin x = √2 / 2 for x ∈ [0, 2π]. (10 points)
- Question 5a: Find the general solution of cos(7x) = 1/2. (10 points)
- Question 5b: Find the general solution of tan(x - 4) = -1/√3. (6 points)
- Question 6: Evaluate limits using the provided graph. (9 points)
- a) f(-6)
- b) lim f(x) as x approaches -1
- c) lim f(x) as x approaches 6+
- d) lim f(x) as x approaches -6
- e) Discontinuities of f(x) on the interval (-9, 9)
- Question 7a: Evaluate lim (-x² + 1) / (x - 1 - x² + x + 2) as x approaches -1. (7 points)
- Question 7b: Evaluate lim |2x - 3| / (x - 2) as x approaches 2. (4 points)
- Question 8: Find values of a and b for a continuous function. f(x) is defined as: { x² + 7, if x < -2; a, if x = -2; bx - 1, if x > -2} (12 points)
- Question 9: Find the value of k that makes the function continuous at x = -9. f(x) is defined as: { (x² + 7x - 18) / (x² + 8x - 9), if x ≠-9; k, if x = -9} (12 points)
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