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Resources

Solve trigonometric equations II

1

. Consider ise following

5

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(i) Statement (ii) is true.

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(ii) At most one of these

5

statements is true.

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5

of these statements are true.

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The last two statements are invisible. Which of the following is correct?

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(A) Only statement (i) is true.

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(B) Only statement (ii) is true.

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(C) Only one of statements (iv) or (v) is true.

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(D) Both statements (iv) and (v) are true.

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(E) Neither of statements (iv) and (v) are true.

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\csc(\theta) = -1

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\_\_\_\_\,^\circ

Find the slope and

y

-intercept of the line whose equation is given

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\mathrm{x}=8

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Determine the slope. Select the correct choice below and fill in any an

Find the areas of the sectors formed by

\angle A C B

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Give the exact answers in terms of

\pi

. Do not approximate the answers.

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Area of small sector

=

\square

\mathrm{ft}^{2}

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Area of large sector

=

\square

\mathrm{ft}^{2}

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The diagram shows different shapes. What conclusions can be drawn based on the markings in the diagram?

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Select the correct answer from each drop-down menu.

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The diagram has

\square

set(s) of parallel line segments and

\square

set(s) of perpendicular line segments.

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The diagram has

\square

set(s) of congruent angles and set(s) of congruent segments.

Make a calculation totaling the figure below by inserting the four mathematical operators

(+,-, \div, x)

between the numbers shown. They can be inserted in any order, and one of them has been used twice.

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Here's a trickier one! Using the same principle as above

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\qquad

6

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\qquad

\qquad

5

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Dlrections: Find each missing measure.

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Directions: find the value of

x

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7

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Directions: Classify each triangle by its angles and sides.

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12

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Directlons: Determine whether the statement is always, sometimes, or never true.

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13

. If a triangle is acute, then it is an equilateral triangle.

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14

. If a triangle has two acute angles it must be an acute triangle.

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15

. An obtuse triangle can have a right angle.

Find all solutions with

-90° \leq \theta \leq 90°

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\sin (\theta) = \frac{1}{2}

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Find all solutions with

-90^\circ < \theta < 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\tan (\theta) = 0

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\_\_\_\_\,^\circ

Find all solutions with

-90^\circ < \theta < 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\tan (\theta) = 1

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\_\_\_\_\,^\circ

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\cos (\theta) = \frac{1}{2}

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\_\_\_\_\,^\circ

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\sin (\theta) = 1

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\_\_\_\_\,^\circ

Find all solutions with

-90^\circ < \theta < 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\tan (\theta) = -1

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\_\_\_\_\,^\circ

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\cos (\theta) = 0

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\_\_\_\_\,^\circ

Find all solutions with

-90° \leq \theta \leq 90°

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\sin (\theta) = 0

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\_\_\_\_°

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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\sin (\theta) = -1

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\_\_\_\_\,^\circ

6

: Area, Surface Area, and Volume Study Guide

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Directions: Complete all problems showing your work. Don'

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1

.) Find the total area of the figure shown.

\pi

is defined as the ratio of the circumference (say,

c

) of a circle to its diameter (say

d

\pi = \frac{c}{d}

. This seems to contradict the fact that

\pi

is irrational. How will you resolve this contradiction?

H

is the midpoint of

I G

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J

is the midpoint of

I K

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I G=G K=10

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\frac{\text { Quantity A }}{I J}

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5

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Quantity A is greater.

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Quantity B is greater.

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The two quantities are equal.

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The relationship cannot be determined from the information given.

What is the confidence level of each of the following confidence intervals for

\mu

? Complete parts a through e.

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E Click the icon to view the table of normal curve areas.

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\bar{x}\pm1.96\left(\frac{\sigma}{\sqrt{n}}\right)

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% (Round to two decimal places as needed.)

What is the confidence level of each of the following confidence intervals for

\mu

? Complete parts a through

\mathbf{e}

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] Click the icon to view the table of normal curve areas.

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\bar{x} \pm 1.96\left(\frac{\sigma}{\sqrt{n}}\right)

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\%

(Round to two decimal places as needed.)

The table gives selected values of the differentiable function

f

. Below is Leo's attempt to write a formal justification for the fact that there exists a value

c

a < c < b

f'(c) = \frac{f(b) - f(a)}{b - a}

. Is Leo's justification complete? If not, why? Leo's justification:

f

is differentiable on

[a, b]

. So, according to the mean value theorem, there exists a value

c

somewhere between

a

b

f'(c) = \frac{f(b) - f(a)}{b - a}

Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triangle, or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth.

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A=35^\circ \quad a=24 \quad b=19

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Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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A. There is only one possible solution for the triangle.

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The measurements for the remaining angles

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B

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C

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c

are as follows.

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B=\square^\circ

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C=\square^\circ

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(Round to the nearest tenth as needed.)

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c=\square

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B. There are two possible solutions for the triangle.

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The measurements for the solution with the longer side

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c

are as follows.

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B_{1}=\square^\circ

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C_{1}=\square^\circ

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B

0

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The measurements for the solution with the shorter side

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c

are as follows.

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B

2

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B

3

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(Round to the nearest tenth as needed.)

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C. There are no possible solutions for the triangle.

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View an example

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Get more help -

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Learn with an example

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\checkmark

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or Watch a video (D)

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The diagram shows a convex polygon.

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What is the sum of the exterior angle measures, one at each vertex, of this polygon?

\circ

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24

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What are the critical points for the plane curve defined by the equations

x(t)=-\sin (3 t), y(t)=5 t

0 \leq t<\pi

? Write your answer as a list of values of

t

, separated by commas. For example, if you found

t=1

t=2

, you would enter

1

2

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Provide your answer below:

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MORE INSTRUCTION

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Content attribution

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-x-2y=0

is graphed in the

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xy

-plane. Which of the following is a true statement about the graph?

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1

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(A) The graph goes through the point

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(-1,2)

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(B) The graph has a slope of

2

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(C) The graph goes through the point

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(0,0)

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(D) The graph has a slope of

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\frac{1}{2}

Kajal tried to solve the differential equation

\frac{d y}{d x}=-x^{2} y^{2}

. This is her work:

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\frac{d y}{d x}=-x^{2} y^{2}

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1

\quad \int-y^{-2} d y=\int x^{2} d x

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2

\quad y^{-1}=\frac{x^{3}}{3}+C

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3

\quad y=\frac{3}{x^{3}}+C

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Is Kajal's work correct? If not, what is her mistake?

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1

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(A) Kajal's work is correct.

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1

is incorrect. The separation of variables wasn't done correctly.

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2

is incorrect. Kajal didn't integrate

x^{2}

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3

is incorrect. Kajal didn't take the reciprocal of

\frac{x^{3}}{3}+C

Evaluate. Write your answer in simplified, rationalized form. Do not round.

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\cot 30^\circ =

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

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\_\_\_\_\,^\circ