Radians to Degrees and The Unit Circle

30°

π/6

45°

π/4

90°

π/2

60°

π/3

120°

2π/3

135°

3π/4

150°

5π/6

180°

π

210°

7π/6

225°

5π/4

240°

4π/3

270°

3π/2

300°

5π/3

315°

7π/4

330°

11π/6

360°

2π

π/6

30°

π/4

45°

π/3

60°

π/2

90°

2π/3

120°

3π/4

135°

5π/6

150°

π

180°

7π/6

210°

5π/4

225°

4π/3

240°

3π/2

270°

5π/3

300°

7π/4

315°

11π/6

330°

2π

360°

If there is a 6 in the denominator, what type of degree must the angle be?

30°

If there is a 4 in the denominator, what type of degree must the angle be?

45°

If there is a 3 in the denominator, what type of degree must the angle be?

60°

Sine (Sin) equals what?

y

Cosine (Cos) equals what?

x

Secant (Sec) equals what?

1/x

Cosecant (Csc) equals what?

1/y

Cotangent (Cot) equals what?

x/y

Tangent (Tan) equals what?

y/x

What is the saying to help remember the positivity of a trigonometric function in a particular quadrant?

All Students Take Calculus (ASTC)

If Tan(45), then what must the answer be?

1 or -1

In a 30-60-90 triangle, the shortest leg will always be opposite of what angle?

30°

In a 30-60-90 triangle, the longest leg will always be opposite of what angle?

60°

In a 30-60-90 triangle, the longest side (hypotenuse) will always be opposite of what angle?

90°

What are some (4) Pythagorean Triples?

1. 3-4-5

2. 5-12-13

3. 7-24-25

4. 8-15-17

What is the mnemonic used to remember the side of Sine, Cosine, and Tangent?

SohCahToa

What are the six trig functions?

1. Sine

2. Cosine

3. Tangent

4. Secant

5. Cosecant

6. Cotangent

Sin(θ) =

opposite/hypotenuse

Cos(θ) =

adjacent/hypotenuse

Tan(θ) =

opposite/adjacent

Secant(θ) =

hypotenuse/adjacent

Cosecant(θ) =

hypotenuse/opposite

Cotangent(θ) =

adjacent/opposite

The Unit Circle goes in a _____________________________ direction

Counterclockwise

On the Unit Circle, what is the coordinate point at 0°?

(1,0)

On the Unit Circle, what is the coordinate point at 30°?

(√3/2, 1/2)

On the Unit Circle, what is the coordinate point at 45°?

(√2/2, √2/2)

On the Unit Circle, what is the coordinate point at 60°?

(1/2, √3/2)

On the Unit Circle, what is the coordinate point at 90°?

(0, 1)

On the Unit Circle, what is the coordinate point at 120°?

(-1/2, √3/2)

On the Unit Circle, what is the coordinate point at 135°?

(-√2/2, √2/2)

On the Unit Circle, what is the coordinate point at 150°?

(-√3/2, 1/2)

On the Unit Circle, what is the coordinate point at 180°?

(-1, 0)

On the Unit Circle, what is the coordinate point at 210°?

(-√3/2, -1/2)

On the Unit Circle, what is the coordinate point at 225°?

(-√2/2, -√2/2)

On the Unit Circle, what is the coordinate point at 240°?

(-1/2, -√3/2)

On the Unit Circle, what is the coordinate point at 270°?

(0, -1)

On the Unit Circle, what is the coordinate point at 300°?

(1/2, -√3/2)

On the Unit Circle, what is the coordinate point at 315°?

(√2/2, -√2/2)

On the Unit Circle, what is the coordinate point at 330°?

(√3/2, -1/2)

On the Unit Circle, what is the coordinate point at 360°?

(1, 0)