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Honors Analysis Section 7.2: Trigonometric Functions of General Angles Q Problems Q1.) How many committees of 4 people can be selected from a group of 6 people? Q2.) How many ways can 5 students be seated around a circular table? Q3.) What is the probability of rolling a sum of 8 on two fair, six-sided dice? Q4.) A linear function exists such that f(0) = 20 and f(4) = 0. What is f(10)? Q5.) 5−3 = Q6.) Convert 45 mph to ft/s. Q7.) What is the GCF of 28352 and 8960? (Hint: Use the prime factorizations!) Q8.) What is the LCM of the numbers from Q7? Q9.) Benji rode his bike 30 miles. If he increased his speed by 3 mph, he would have decreased his travel time by 20 minutes. What was his original speed? Q10.) Solve for y: 1.) Give the algebraic definitions of the six trigonometric functions when graphed in standard position on the coordinate plane (use x, y, and r, where 𝑟 = √𝑥 2 + 𝑦 2 ). Give the exact values of the six trigonometric functions of angle 𝜃 if the terminal side of the angle contains the given point. 2.) (3, -4) 3.) (-15, 8) 4.) (7, 24) 5.) (6, 6) 6.) (-4, 0) 7.) (2, 4) Sketch each angle in standard position. Then determine its reference angle. 5𝜋 8.) 250º 9.) 140º 10.) -240º 11.) 4 12.) Determine the exact value of each trig function: 13.) sin 150º 14.) cos 300º 15.) tan 135º 16.) cos 180º 19.) tan 90º 20.) sec 17.) 𝑐𝑜𝑠 5𝜋 6 18.) tan 7𝜋 4 21.) tan 5𝜋 3 22.) cot 510º 23.) cos 11𝜋 3 2𝜋 3 7𝜋 6 24.) csc 450º Suppose 𝜃 is an angle in standard position whose terminal side is in the given quadrant. For each function, find the exact values of the remaining five trigonometric functions of 𝜃. 3 12 8 25.) cos θ = 5, Quadrant 1 26.) tan 𝜃 = − 5 , Quadrant II 27.) sin θ = 17 , Quadrant II 1 28.) cot 𝜃 = 2 , Quadrant III 29.) sec 𝜃 = −√10, Quadrant IV 30.) csc 𝜃 = −5, Quadrant IV Given that angle 𝜃 is graphed in standard position, state the quadrant or quadrants in which the terminal side lies: 31.) sin 𝜃 > 0 32.) tan 𝜃 < 0 33.) sin 𝜃 > 0, cos 𝜃 < 0 34.) tan 𝜃 > 0, cos 𝜃 < 0 Find two values of x that make each statement true: 35.) cos x = 1 36.) sin x = 1 37.) cos x = 0 38.) sin x = 0 39.) cos x = -1