Question 1

Which of the following describes the general solution to the equation

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 2

If

\sin(x) + \cos(x) = \sqrt{2}

, which of the following expressions is equivalent to

\sin(2	heta)

in terms of

t

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 3

Given that

\sin(x) + \cos(x) = \sqrt{2}

, which of the following expressions represents the values of

\sin(2	heta)

according to De Moivre's Theorem for roots?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

for

k = 0, 1, ..., n-1

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

for

k = 0, 1, ..., n-1

Answer

x = 2n\pi + \frac{\pi}{4}

Question 4

What is the value of the product

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 5

Which of the following identities correctly expresses

\sin(x) + \cos(x) = \sqrt{2}

in terms of

\sin(2	heta)

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 6

What is the exact value of the expression

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 7

In a triangle

\sin(x) + \cos(x) = \sqrt{2}

, if the side lengths are

\sin(2	heta)

,

t

, and

c = 8

, what is the measure of angle

B

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 8

What is the exact value of

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 9

What is the period of the trigonometric function

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

5

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 10

Which of the following is the correct evaluation of the limit

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

0

Answer

1

Answer

x = 2n\pi + \frac{\pi}{4}

Question 11

Which of the following expressions is equivalent to

\sin(x) + \cos(x) = \sqrt{2}

in terms of

\sin(2	heta)

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 12

Given a triangle with sides

\sin(x) + \cos(x) = \sqrt{2}

,

\sin(2	heta)

, and

t

, what is the value of

c = 8

where

B

is the angle opposite side

a

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 13

Which of the following values is the result of the expression

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 14

Determine the general solution for the equation

\sin(x) + \cos(x) = \sqrt{2}

.

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 15

If

\sin(x) + \cos(x) = \sqrt{2}

and

\sin(2	heta)

is in the second quadrant, what is the value of

t

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 16

Which of the following expressions is the correct period of the function

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 17

Which of the following describes the complete set of solutions for the equation

\sin(x) + \cos(x) = \sqrt{2}

over the interval

\sin(2	heta)

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 18

Which of the following describes the relationship between

\sin(x) + \cos(x) = \sqrt{2}

and

\sin(2	heta)

correct for all values of

t

in their domains?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 19

If

\sin(x) + \cos(x) = \sqrt{2}

and

\sin(2	heta)

, what is the value of

t

?

Accepted Answer

1

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Question 20

What is the exact value of

\sin(x) + \cos(x) = \sqrt{2}

?

Accepted Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

Answer

x = 2n\pi + \frac{\pi}{4}

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