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

HW Answers: Pg377- 8 (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=− 15 17 , 𝑐𝑜𝑠𝑡= 8 17 , 𝑡𝑎𝑛𝑡=− 15 8 , 𝑐𝑠𝑐𝑡=− 17 15 , 𝑠𝑒𝑐𝑡= 17 8 , 𝑐𝑜𝑡𝑡=− 8 15 5) 2 2 , 2 2 7) − 3 2 , 1 2 9) − 1 2 ,− 3 2 11) (0, -1) 13) 𝑠𝑖𝑛 𝜋 4 = 2 2 , 𝑐𝑜𝑠 𝜋 4 = 2 2 , tan 𝜋 4 =1 15) 𝑠𝑖𝑛 − 𝜋 6 =− 1 2 , 𝑐𝑜𝑠 − 𝜋 6 = 3 2 , tan − 𝜋 6 =− 3 3 17) 𝑠𝑖𝑛 − 5𝜋 4 =− 2 2 , 𝑐𝑜𝑠 − 5𝜋 4 =− 2 2 , tan − 5𝜋 4 =−1 19) 𝑠𝑖𝑛 11𝜋 6 =− 1 2 , 𝑐𝑜𝑠 11𝜋 6 = 3 2 , tan 11𝜋 6 =− 3 3 21) 𝑠𝑖𝑛 4𝜋 3 =− 3 2 , 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 = 2 2 , 𝑐𝑜𝑠 3𝜋 4 =− 2 2 , 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 = 3 2 , 𝑐𝑜𝑠 − 4𝜋 3 =− 1 2 , 𝑡𝑎𝑛 − 4𝜋 3 =− 3 , 𝑐𝑠𝑐 − 4𝜋 3 = 2 3 3 , 𝑠𝑒𝑐 − 4𝜋 3 =−2, 𝑐𝑜𝑡 − 4𝜋 3 =− 3 3 32) -1 36) -1/2 40) a. -2/5 b. -5/2 46) 0 50) 1.3410

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

The Unit Circle: Radian Measures and Coordinates

Right Triangle Definitions of Trigonometric Functions hyp opp  adj

Example: Find the six trig functions of . Pythagorean Theorem (opp)2 + (adj)2 = (hyp)2 42 + 32 = hyp2 5 = hyp 5 4  3

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

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

Fundamental Trigonometric Identities: Reciprocal Identities: Quotient Identities: Pythagorean Identities:

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

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

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

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

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

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