Reference Angles

Unit 5: Trigonometry

5.7 Reference Angles and the Unit Circle

Fill in the Blanks

Find the length of BC. Round to the nearest tenth.

1. Reference Angle (α)

• Any angle around a circle can be turned into a right triangle using a reference angle (α).

• Using this we can calculate any angle around the center of a circle.

• Depending on the Quadrant (I, II, III, IV) the initial side of the refence angle changes.

​How to find the angle using a reference angle by quadrant:

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Multiple Choice

What is the reference angle for 275°?

• 85°

• 95°

• -85°

• -95°

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the reference angle?

• 163

• 73

• 27

• 107

Multiple Choice

What is the reference angle?

• 43

• -43

• 47

• -47

2. Finding Trig Ratios using reference angles and a unit circle.

• Unit Circle- all the angles around the origin of a circle that can be used to form a right triangle.

• We can use the unit circle and special right triangles to find the values of common angles trig ratios.

​Special Right Triangles you should know:

​1

​1

​1

​-1

​1

​-1

​1

​-1

I II III IV

All Students Take Calculus

​All are +.

​Sine is +.

Tangent is +.

Cosine is +.

Multiple Select

Which trigonometric functions are positive for the angle 112°?

• Sine

• Cosine

• Tangent

• Cosecant

• Secant

Multiple Select

Which trigonometric functions are positive for the angle 315°?

• Sine

• Cosine

• Tangent

• Cosecant

• Secant

Multiple Select

Which trigonometric functions are positive for the angle 208°?

• Sine

• Cosine

• Tangent

• Cosecant

• Cotangent

Multiple Select

Which trigonometric functions are positive for the angle 38°?

• Sine

• Cosine

• Tangent

• Cosecant

• Cotangent

3. Using the Unit Circle.

The Unit Circle is used to find the sine, cosine and tangent values for all the angles around the circle with a reference angle of 30°, 45°, 60° and 90°.

Ex. Find the sine, cosine and tangent of 300°.

Math Response

What is the sine value of 210°?

Type answer here

Correct Answer: \frac{-1}{2}

Deg^°

Rad

Math Response

What is the cosine value of 210°?

Type answer here

Correct Answer: \frac{-\sqrt{3}}{2}

Deg^°

Rad

Math Response

What is the tangent value of 210°?

Type answer here

Correct Answer: \frac{\sqrt{3}}{3}

Deg^°

Rad

Math Response

What is the sine value of 30°?

Type answer here

Correct Answer: \frac{1}{2}

Deg^°

Rad

Math Response

What is the cosine value of 30°?

Type answer here

Correct Answer: \frac{\sqrt{3}}{2}

Deg^°

Rad

Math Response

What is the tangent value of 30°?

Type answer here

Correct Answer: \frac{\sqrt{3}}{3}

Deg^°

Rad

Math Response

What is the sine value of 135°?

Type answer here

Correct Answer: \frac{\sqrt{2}}{2}

Deg^°

Rad

Math Response

What is the cosine value of 135°?

Type answer here

Correct Answer: \frac{-\sqrt{2}}{2}

Deg^°

Rad

Math Response

What is the tangent value of 135°?

Type answer here

Correct Answer: -1

Deg^°

Rad