Unit 5 Interim Review

5.1

100

Simplify the Trig Expression:

tan(θ)cos(θ)

sin(θ)

200

sin(θ)csc(θ) - sin²(θ)

cos²(θ)

300

Simplify the Trig Expression:

(secθ/cscθ) + (sinθ/cosθ)

2tanθ

400

(sin⁴x - cos⁴x) / (sin²x - cos²x)

1

500

Simplify the Trig Expression:

sec(-x) + tan(-x)cos(𝝅/2 - x)

cos(x)

5.2

100

(1 + cosx)/(sinx) = cscx + cotx

(1 + cosx)/(sinx) = 

(1/sinx) + (cosx/sinx) = 

cscx + cotx

200

Verify the Trig Identity:

cosx(tan²x + 1) = sec(x)

cosx(tan²x + 1) 

cosx(sec²x)

cosx(1/cos²x)

1/cosx

sec(x)

300

(1 - tan²x)/(1 + tan²x) = 1-2sin²x

(1 - tan²x)/(1 + tan²x) = 

(1 - tan²x)/(sec²x) = 

(1 / sec²x) - (tan²x/sec²x) = 

cos²x - sin²x = 

(1 - sin²x) - sin²x = 

1 - 2sin²x

400

Verify the Trig Identity:

(sinx + cosx)² + (sinx - cosx)² = 2

(sinx + cosx)² + (sinx - cosx)²

sin²x + 2cosxsinx + cos²x + sin²x - 2cosxsinx + cos²x 

2sin²x + 2cos²x

2(sin²x + cos²x)

2(1)

2

500

Verify the Trig Identity:

(1/(sinx - 1)) - (1/(sinx + 1)) = -2sec²x 

(1/(sinx - 1)) - (1/(sinx + 1)) =

(sinx + 1 - sinx + 1)/(sin²x -1) =

2/(-cos²x) = 

-2sec²x

5.3

100

Solve the Equation on the interval [0,2π)

2cos²θ = sinθ + 1

π, π/6, 3π/2

200

Solve the equation over the interval [0,2π)

4sin²(3θ) - 3 = 0

π/9, 2π/9, 4π/9, 5π/9

300

Solve the equation and give the general solution:

4cosx = 1 + 2cosx

π/3 = 2πn, 5π/3 + 2πn

where n is an integer

400

Solve the equation over the interval [0,2π)

3tan⁴x- 10tan²x = -3

π/6, 5π/6, 7π/6, 11π/6, π/3, 2π/3, 4π/3, 5π/3

500

Solve the equation and give the general solution:

2sin(3x) - √2 = 0

π/12 + (2πn)/3, π/4 + (2πn)/3

Where n is an integer

Identifying Identities

100

What type of Identity is this:

cscθ = 1/sinθ

Reciprocal Identity

200

What type of Identity is this:

sin²θ + cos²θ = 1

Pythagorean Identity

300

What type of Identity is this:

tanθ = sinθ/cosθ

Ratio Identity

400

What type of Identity are these:

cos(-θ) = cosθ & sin(-θ) = -sinθ

Even/Odd Formulas

500

What type of Identity are these:

cos(π/2 - θ) = sinθ

Cofunction Identity

Trig Trivia

100

Sine, cosine, and tangent are all positive in this quadrant.

Quadrant 1

200

Simplify sin(π/6)

1/2

300

Simplify tan(2π/3)

√3

400

The cosine of an angle is equal to √2/2 at these two angles.

Pi/4 and 7Pi/4 (45 and 315 degrees).

500

On the unit circle, you can find tangent this way.

What is divide y by x?