TA N G E N T

THE UNIT CIRCLE

REMEMBER

• Find x in the right triangle above.

x

1

30°

• Find y in the right triangle below.

y

• Using your calculator, what is the cos 30°?

• Using your calculator, what is the sin 30°?

Aim: Know exact values of critical angles in order to simplify expressions.

≈ 0.8660

0.5

TANGENT

• According to SohCahToa

= cosθ

1

θ

Aim: Know exact values of critical angles in order to simplify expressions.

Cah

Toa

x

y = sinθ

Soh

QUADRANT I

30°

1

0° 30°

45°

60°

90°

sinθ

cosθ

tan θ

0° 30°

45°

60°

90°

sinθ

cosθ

tan θ

Exact Values

Approximate Values

145°

1

60°

1

90°

1

Aim: Know exact values of critical angles in order to simplify expressions.

ON THE UNIT CIRCLE

sinθ θ

cosθ

tanθ

θ

θ θ

Aim: Know exact values of critical angles in order to simplify expressions.

WHERE ARE THE POSITIVES?

AllStudents

Take Calculus

Sin

Tan

Cos

All

Aim: Know exact values of critical angles in order to simplify expressions.

TRY THESE

1. If cosθ > 0 and tanθ < 0, which quadrant is the terminating ray of an angle in standard position.

2. The point is on the terminal side of an angle θ in standard position. If the distance of the point from the origin is one unit, find sinθ and tanθ.

3. Find the exact value of sin (-135°).

4. Simplify: (cos 30°)(sin 60°) – tan 60°

Aim: Know exact values of critical angles in order to simplify expressions.