Podcast
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].
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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) = $\frac{1}{2}$
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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 - $\frac{\pi}{4}$) = $\frac{-1}{\sqrt{3}}$
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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)
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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-
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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).
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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-
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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→($\frac{3}{2}$)+
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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) = {$\begin{matrix} \frac{x^2 +4}{3} & , if x<-2 \ -2 & , if x=-2 \ bx-1 & , if x>-2 \end{matrix}$
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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) = {$\begin{matrix} \frac{x^2+7x-18}{x^2 + 8x-9} & , for x≠-9 \ k & , for x = -9 \end{matrix}$
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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)
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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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Description
This quiz tests your understanding of trigonometric identities and limit evaluations. You'll need to demonstrate your problem-solving skills by showing your work clearly and indicating the method used to arrive at each answer. Be sure to check your units and the accuracy of your answers.
