1. Warm-up:
Find the tan 5𝜋 3
HW: pg.387 (2 – 16 even, 33 – 36, 37 – 39, 47 – 52, 59 – 66)

2. HW Answers: Pg (1 – 29 odd, 32, 36, 40, 46, 50)
1) 𝑠𝑖𝑛𝑡= 4 5 , 𝑐𝑜𝑠𝑡=− 3 5 , 𝑡𝑎𝑛𝑡=− 4 3 , 𝑐𝑠𝑐𝑡= 5 4 , 𝑠𝑒𝑐𝑡=− 5 3 , 𝑐𝑜𝑡𝑡=− 3 4
3) 𝑠𝑖𝑛𝑡=− , 𝑐𝑜𝑠𝑡= 8 17 , 𝑡𝑎𝑛𝑡=− 15 8 , 𝑐𝑠𝑐𝑡=− , 𝑠𝑒𝑐𝑡= 17 8 , 𝑐𝑜𝑡𝑡=− 8 15
5) , ) − , ) − 1 2 ,− ) (0, -1)
13) 𝑠𝑖𝑛 𝜋 4 = , 𝑐𝑜𝑠 𝜋 4 = , tan 𝜋 4 =1
15) 𝑠𝑖𝑛 − 𝜋 6 =− 1 2 , 𝑐𝑜𝑠 − 𝜋 6 = , tan − 𝜋 6 =−
17) 𝑠𝑖𝑛 − 5𝜋 4 =− , 𝑐𝑜𝑠 − 5𝜋 4 =− , tan − 5𝜋 4 =−1
19) 𝑠𝑖𝑛 11𝜋 6 =− 1 2 , 𝑐𝑜𝑠 11𝜋 6 = , tan 11𝜋 6 =−
21) 𝑠𝑖𝑛 4𝜋 3 =− , 𝑐𝑜𝑠 4𝜋 3 =− 1 2 , tan 4𝜋 3 = 3
23) 𝑠𝑖𝑛 − 3𝜋 2 =1, 𝑐𝑜𝑠 − 3𝜋 2 =0, tan − 3𝜋 2 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
25) 𝑠𝑖𝑛 3𝜋 4 = , 𝑐𝑜𝑠 3𝜋 4 =− , 𝑡𝑎𝑛 3𝜋 4 =−1, 𝑐𝑠𝑐 3𝜋 4 = 2 , 𝑠𝑒𝑐 3𝜋 4 =− 2 ,𝑐𝑜𝑡 3𝜋 4 =−1
27)𝑠𝑖𝑛 𝜋 2 =1, 𝑐𝑜𝑠 𝜋 2 =0, 𝑡𝑎𝑛 𝜋 2 =𝑢𝑛𝑑𝑒𝑓, 𝑐𝑠𝑐 𝜋 2 =1, 𝑠𝑒𝑐 𝜋 2 =𝑢𝑛𝑑𝑒𝑓,𝑐𝑜𝑡 𝜋 2 =0
29) 𝑠𝑖𝑛 − 4𝜋 3 = , 𝑐𝑜𝑠 − 4𝜋 3 =− 1 2 , 𝑡𝑎𝑛 − 4𝜋 3 =− 3 ,
𝑐𝑠𝑐 − 4𝜋 3 = , 𝑠𝑒𝑐 − 4𝜋 3 =−2, 𝑐𝑜𝑡 − 4𝜋 3 =−
32) -1
36) -1/2
40) a. -2/5
b. -5/2
46) 0
50)

3. 4.3 Right Triangle Trigonometry
Objective:
Evaluate 6 trigonometric functions
Identify Trigonometric Identities
Evaluate trigonometric functions with a calculator.
Applications Involving right triangles

4. The Unit Circle: Radian Measures and Coordinates

5. Right Triangle Definitions of Trigonometric Functions
hyp
opp 
adj

6. Example: Find the six trig functions of . Pythagorean Theorem
(opp)2 + (adj)2 = (hyp)2
= hyp2
= hyp 5 4  3

7. Example: Evaluate Trig functions of 45. Pythagorean Theorem
(1)2 + (1)2 = (ℎ𝑦𝑝)2
2 = hyp2
2 = hyp
45 2 1
45 1

8. Example:
Evaluate Trig functions of 60.
30 2 3
60 1

9. Fundamental Trigonometric Identities:
Reciprocal Identities:
Quotient Identities:
Pythagorean Identities:

10. Applying Trig Identities:
Let  be an acute angle such that sin = Find the values of
a) cos and b) tan using trig identities. 1
0.6 
0.8

11. Applying Trig Identities:
Let  be an acute angle such that tan = 3 Find the values of
a) cot and b) sec using trig identities. 10 3  1

12. Solving a Right Triangle
Ex) A surveyor is standing 50 ft from the base of a large tree. The measure of elevation to the top of the tree is 71.5. How tall is the tree? x
71.5
50ft

13. Ex) A person is 200 yards from a river
Ex) A person is 200 yards from a river. The person walks 400 yards along a straight path to the rivers edge. Find the acute angle  between the river and the path. 
200yd
From unit circle:
400yd

14. Ex) A 12m flagpole casts a 9m shadow, Find the angle of elevation of the sun.
Calculator:
Tan-1 (  Enter
12m  9m

15. Sneedlegrit: Find  using a trig ratio.4 2 
HW: pg.387 (2 – 16 even, 33 – 36, 37 – 39, 47 – 52, 59 – 66)