# Pre Calculus Trigonometric Functions

*label*Mathematics

*timer*Asked: Dec 20th, 2017

*account_balance_wallet*$15

**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.

## Tutor Answer

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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