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Converting Angles Finding Angles Coterminal/ Reference ∠’s Exact Values (Trig Functs) Finding Trig Ratios $100 $100 $100 $100 $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500 $500 $500

$100 Converting Angles Question: Convert from degrees to radians 320° Answer: 16𝜋 9

$200 Converting Angles Question: Convert from degrees to radians 80° Answer: 4𝜋 9

$300 Converting Angles Question: Convert from degrees to radians 675° Answer: 15𝜋 4

$400 Converting Angles Question: Convert from radians to degrees 8𝜋 3 Answer: 480°

$500 Converting Angles Question: Convert from radians to degrees 15𝜋 12 Answer: 225°

$100 Finding Angles cos 𝜃 = 2 2 𝜃= 𝜋 4 , 7𝜋 4 Question: Find the measure of θ in both radians and degrees given (without a calculator): cos 𝜃 = 2 2 Answer: 𝜃=45°, 315° 𝜃= 𝜋 4 , 7𝜋 4

$200 Finding Angles cos 𝜃 = 1 2 𝜃=60° , 300° 𝜃= 𝜋 3 , 5𝜋 3 Question: Find the measure of θ in both radians and degrees given (without a calculator): cos 𝜃 = 1 2 Answer: 𝜃=60° , 300° 𝜃= 𝜋 3 , 5𝜋 3

$300 Finding Angles tan 𝜃 =1 𝜃=45°, 225° 𝜃= 𝜋 4 , 5𝜋 4 Question: Find the measure of θ in both radians and degrees given (without a calculator): tan 𝜃 =1 Answer: 𝜃=45°, 225° 𝜃= 𝜋 4 , 5𝜋 4

$400 Finding Angles csc 𝜃 = 2 3 3 𝜃=60° , 120° 𝜃= 𝜋 3 , 2𝜋 3 Question: Find the measure of θ in both radians and degrees given (without a calculator): csc 𝜃 = 2 3 3 Answer: 𝜃=60° , 120° 𝜃= 𝜋 3 , 2𝜋 3

$500 Finding Angles cot 𝜃 = 3 3 𝜃=60° , 240° 𝜃= 𝜋 3 , 4𝜋 3 Question: Find the measure of θ in both radians and degrees given (without a calculator): cot 𝜃 = 3 3 Answer: 𝜃=60° , 240° 𝜃= 𝜋 3 , 4𝜋 3

$100 Coterminal/ Reference ∠’s Question: Determine two coterminal angles (one positive and one negative) for: 230° Answer: 590° , −130°

$200 Coterminal/ Reference ∠’s Question: Determine two coterminal angles (one positive and one negative) for: 5𝜋 6 Answer: 17𝜋 6 , − 7𝜋 6

$300 Coterminal/ Reference ∠’s Question: Determine two coterminal angles (one positive and one negative) for: − 11𝜋 6 Answer: 𝜋 6 , − 23𝜋 6

$400 Coterminal/ Reference ∠’s Question: Find the reference angle of the given angle measurement: 7𝜋 4 Answer: 𝜋 4

$500 Coterminal/ Reference ∠’s Question: Find the reference angle of the given angle measurement: 11𝜋 3 Answer: 𝜋 3

$100 Exact Values (Trig Functions) Question: Find the exact value of cos 11𝜋 6 Answer: 3 2

$200 Exact Values (Trig Functions) Question: Find the exact value of sin 5𝜋 4 Answer: − 2 2

$300 Exact Values (Trig Functions) Question: Find the exact value of tan 585° Answer: 1

$400 Exact Values (Trig Functions) Question: Find the exact value of sec 720° Answer: 2 3 3

$500 Exact Values (Trig Functions) Question: Find the exact value of cot − 5𝜋 6 Answer: 3

$100 Finding Trig Ratios Question: Find the six trig functions given the point (3, 4) Answer: sin 𝜃 = 4 5 cos 𝜃 = 3 5 tan 𝜃 = 4 3 csc 𝜃 = 5 4 sec 𝜃 = 5 3 cot 𝜃 = 3 4

$200 Finding Trig Ratios Question: Find the six trig functions given the point (0, 6) Answer: sin 𝜃 =1 cos 𝜃 =0 tan 𝜃 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 csc 𝜃 =1 sec 𝜃 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 cot 𝜃 =0

$300 Finding Trig Ratios Question: Find the six trig functions given the point (-5, 12) Answer: sin 𝜃 = 12 13 cos 𝜃 =− 5 13 tan 𝜃 =− 12 5 csc 𝜃 = 13 12 sec 𝜃 =− 13 5 cot 𝜃 =− 5 12

$400 Finding Trig Ratios Question: Find the six trig functions given: sec 𝜃 = 17 15 , 𝑄𝑢𝑎𝑑 𝐼𝑉 Answer: sin 𝜃 =− 8 17 cos 𝜃 = 15 17 tan 𝜃 =− 8 15 csc 𝜃 =− 17 8 sec 𝜃 = 17 15 cot 𝜃 =− 15 8

$500 Finding Trig Ratios Question: Find the six trig functions given: sin − 3 3 , 𝑄𝑢𝑎𝑑 𝐼𝐼𝐼 Answer: sin 𝜃 =− 3 3 cos 𝜃 =− 6 3 tan 𝜃 = 2 2 csc 𝜃 =− 3 sec 𝜃 =− 6 2 cot 𝜃 = 2