Download IB Math SL- 11 Lesson: Reference Angles Objectives: Students will

IB Math SL- 11
Lesson: Reference Angles
Objectives:
 Students will understand how to find a reference angle for any angle given (both in
degree and radian mode).
 Students will use reference angles to find the exact value of trigonometric expression.
Standards: IBO 3.2
Anticipatory Set:
Teaching Activities:
Reference angles are acute angles that touch the x-axis. Reference angles are always positive
and help us find exact values.
There are four possible locations for reference angles:
The teacher will then model three examples, afterwards the students will try two on their own
(see guided practice).
Examples: Find the exact value
1. 𝑠𝑖𝑛150°
2. 𝑐𝑜𝑠240°
3. 𝑡𝑎𝑛 − 225°
IB Math SL- 11
Students will recall the three reciprocal functions for sine, cosine, and tangent. The teacher will
then model questions 6-8, afterwards students will try 9-10 on their own (see guided practice).
Reciprocal Functions: Find the exact value
6. 𝑐𝑠𝑐
7. 𝑐𝑜𝑡
5𝜋
6
3𝜋
4
𝜋
8. 𝑐𝑠𝑐 (− 6 )
Guided Practice:
Practice: Find the exact value
4. 𝑠𝑖𝑛390°
5𝜋
5. 𝑐𝑜𝑠 3
Practice with reciprocal functions: Find the exact value
5𝜋
9. 𝑠𝑒𝑐 4
10. tan(2𝜋) 𝑠𝑖𝑛
2𝜋
3
𝜋
− 𝑐𝑜𝑠 ( 6 )
Independent Practice:
Students will continue to work on their 5A problem set. Students will also complete the 5.a7
Reference Angles Homework sheet.
Closure:
What are reference angles? Why are reference angles helpful? Can the exact value for all
trigonometric values be found using reference angles?
IB Math SL- 11
Name: _______________________________
4.8 Reference Angles HW
Directions: Find the reference angle for each of the following angles.
1. 315°
3. −
2. −440°
3𝜋
4.
4
25𝜋
4
Directions: Find the exact value
5. 𝑐𝑜𝑠315°
7. 𝑡𝑎𝑛
9.
11𝜋
6
cos(𝑠𝑖𝑛𝜋)
6. cos(−210°)
8. 𝑠𝑖𝑛 (−
10. 𝑡𝑎𝑛
5𝜋
2𝜋
3
6
)
5𝜋
∙ 𝑠𝑖𝑛 ( 3 )
IB Math SL- 11
11. 𝑠𝑖𝑛
11𝜋
6
𝜋
𝑐𝑜𝑠
5𝜋
6
𝜋
12. 2𝑠𝑖𝑛 6 𝑐𝑜𝑠 6
𝜋
3
𝜋
6
𝜋
𝜋
1+𝑡𝑎𝑛 3 𝑡𝑎𝑛 6
𝑡𝑎𝑛 −𝑡𝑎𝑛
13.
− 𝑠𝑖𝑛
5𝜋
6
𝑐𝑜𝑠
11𝜋
6