Pre Calculus Trigonometric Functions

Anonymous
timer Asked: Dec 20th, 2017
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Question description

There are 10 multiple choice questions ranging from: Evaluate the expression. cos(x)sin(90° - x) + sin2(x); What is a factor of: 2sec2(x) - 3sec(x) - 2; Solve the equation for 0 ≤ x < 360. tan2x - tan(x) = 2 that I need help with.

Evaluate the expression. cos(x)sin(90° - x) + sin2(x) 0 1 2x 2sin(x) Evaluate the expression. tan2(x) + sec2(x) 0 1 -1 None of the above. Complete the sentence given below. The factors of sec2(x) - sin2(x) are _______________. sec(x) - sin(x) sec(x) + sin(x) 2(sec(x) - sin(x))(sec(x) + sin(x)) (sec(x) - sin(x))(sec(x) - sin(x)) What is a factor of: 2sec2(x) - 3sec(x) - 2 2sec(x) + 3 2sec(x) + 1 sec(x) - 2 Both B and C What is a factor of: tan2x + 2tan(x)cos(x) + cos2(x) tan(x) + cos(x) tan(x) - cos(x) 2tan(x) - cos(x) Both A and B Solve the equation for 0 ≤ x < 360. tan2x - tan(x) = 2 135 degrees 315 degrees no solution Both A and B Solve the equation for 0 ≤ x < 360. 45 degrees 63 degrees Both A and B Does not exist. Solve the equation for 0 ≤ x < 360. tan(x) + 6 = 3tan(x) + 4 45 and 225 degrees 135 and 315 degrees 135 and 225 degrees 225 and 315 degrees Solve the equation for 0 ≤ x < 360. 45 and 225 degrees 135 and 315 degrees 135 and 225 degrees 225 and 315 degrees Solve the equation for 0 ≤ x < 360. 3csc(x) + 5 = csc(x) + 9 30 and 150 degrees 150 and 330 degrees 60 and 120 degrees 120 and 300 degrees

Tutor Answer

jesusale932
School: Purdue University

Here is my answer :)

Evaluate the expression.
cos(x)sin(90° - x) + sin2(x)

0
1
2x
2sin(x)
cos(𝑥) sin(90º − 𝑥) + sin2 (𝑥) = cos(𝑥) [sin(90º) cos(x) − cos(90º) sin(x)] + sin2 (𝑥)
= cos(𝑥) cos(x) + sin2 (𝑥)
= cos 2 (𝑥) + sin2 (𝑥)
=𝟏

Evaluate the expression.
tan2(x) + sec2(x)

0
1
-1
None of the above.
tan2 (𝑥) + sec 2 (𝑥) = tan2(𝑥) + tan2(𝑥) + 1
= 𝟐 𝐭𝐚𝐧𝟐 (𝒙) + 𝟏

Complete the sentence given below.
The factors of sec2(x) - sin2(x) are _______________.

sec(x) - sin(x)
sec(x) + sin(x)
2(sec(x) - sin(x))(sec(x) + sin(x))
(sec(x) - sin(x))(sec(x) - sin(x))
Let sec(x) = a
Let sin(x) = b
Then,
𝑎2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
So, substituting we get
sec 2 (𝑥) − sin2 (𝑥) = (sec(𝑥) + sin(𝑥))(sec(𝑥) − sin(𝑥))
The factors are:
sec(𝑥) + sin(𝑥)
sec(𝑥) − sin(𝑥)
Answer is: None of the above or Both A and B

What is a factor of: 2sec2(x) - 3sec(x) - 2

2sec(x) + 3
2sec(x) + 1
sec(x) - 2
Both B and C
2 sec 2(𝑥) − 3 sec(𝑥) − 2
3
sec 2 (𝑥) − sec(𝑥) − 1 = 0
2
3
3 2
3 2
sec 2 (𝑥) − sec(𝑥) − 1 + ( ) − ( ) = 0
2
4
4
3
3 2
3 2
sec 2 (𝑥) − sec(𝑥) − 1 + ( ) − ( ) = 0
2
4
4
3
3 2 25
sec (𝑥) − sec(𝑥) + ( ) =
2
4
16
2

3
25
(sec(𝑥) − ( ))2 =
4
16
3
25
sec(...

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Anonymous
Goes above and beyond expectations !

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