Trigonometry Review - Angles in Standard Position

Trigonometry Review Angles in Standard Position 1. Draw and label your two special triangles. Label all three sides and angles. 30-60-90 45-45-90 2. Match each term with its definition from the choices below. reference angle A a formula that relates the lengths of the sides of a triangle to the sine values of its angles B a value that is not an approximation and may involve a radical C the final position of the rotating arm of an angle in standard position D the acute angle formed by the terminal arm and the x-axis E an angle whose vertex is at the origin and whose arms are the x-axis and the terminal arm F a formula that relates the lengths of the sides of a triangle to the cosine value of one of its angles G a situation that is open to two or more interpretations D _________ exact value B _________ sine law A _________ cosine law F ____________ terminal arm C ____________ ambiguous case G _________ angle in standard position E _________ 3. Sketch the following angles in standard position and find their reference angles. a) 𝜃 =150 b) 𝜃 =215 4. Determine the measure of the three other angles in standard position, 0≤ 𝜃 ≤360, that have a reference angle of 35. 325o 5. Point P (2, −6) lies on the terminal arm of angle θ, in standard position. trig ratios for sin 𝜃 , cos 𝜃 , and tan 𝜃 . Determine the exact 6. Point P (12 , −5) lies on the terminal arm of angle θ, in standard position. exact trig ratios for sin 𝜃 , cos 𝜃 , and tan 𝜃 . Determine the 7. Determine the exact value of the following angles: a) sin150o b) tan315o 8. Solve for θ. (Find the values of angle θ, a) cos 𝜃 = − 0≤ 𝜃 ≤360) √3 2 b) sin 𝜃 = − 1 2 𝜽𝟐 = 𝟑𝟔𝟎𝒐 − 𝟑𝟎𝒐 𝜽𝟐 = 𝟑𝟑𝟎𝒐 c) tan 𝜃 = 1 d) cos 𝜃 = 𝜽𝟐 = 𝟏𝟖𝟎𝒐 + 𝟒𝟓𝒐 𝜽𝟐 = 𝟐𝟐𝟓𝒐 1 2 9. The point Q(-3, 6) is on the terminal arm of an angle, θ. a) Draw this angle in standard position. b) Determine the exact distance from the origin to point Q. c) Determine the exact values for sin θ, cos θ, and tan θ. d) Determine the value of θ. 10. A reference angle has a terminal arm that passes through the point P(2, -5). Identify the coordinates of a corresponding point on a different terminal arm for three angles in standard position that have the same reference angle. Sine Law and The Ambiguous Case 11. Determine the number of possible triangles for the following: B 𝑠𝑖𝑛𝐴 = 𝑆𝑖𝑛(139𝑜 ) = 0.65 16 A 139o 14 C 𝐵𝐶 16 = = 1.14 𝐴𝐵 14 𝐵𝐶 >1 𝐴𝐵 1.14 > 1 ∴ 𝑊𝑒 ℎ𝑎𝑣𝑒 𝒐𝒏𝒆 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 12. Solve the triangle: Round your answers to the nearest unit. 𝐶ℎ𝑒𝑐𝑘: 𝑠𝑖𝑛𝐴 = 𝑆𝑖𝑛(30𝑜 ) = 0.5 𝐵𝐶 24 = = 1.14 𝐴𝐶 42 𝐵𝐶 <1 𝐴𝐶 0.5 < 0.57 < 1 𝑆𝑖𝑛𝐴 < ∴ 𝑊𝑒 ℎ𝑎𝑣𝑒 𝒕𝒘𝒐 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠 13. Find side c if, in Cosine Law 14. In triangle . nearest degree. . Find the measure of angle Q to the 15. In triangle nearest tenth. , Find the measure of side d , to the 16. The 12th hole at a golf course is a 375-yd straightaway par 4. When Darla tees off, the ball travels 20° to the left of the line from the tee to the hole. The ball stops 240 yd from the tee (point B). Determine how far the ball is from the centre of the hole. t 17. Two radar stations are tracking the same plane. The angle of elevation from Station A to the plane is 67o, the angle of elevation to the plane from Station B is 82 o. Station A is 3.2 miles from Station B. Find the distances from each station to the plane. What is the altitude of the plane? 𝐚 𝒄 𝐛 𝒄 ∠𝐂 = 𝟏𝟖𝟎 − 𝟖𝟐 − 𝟔𝟕 Altitude of the plane (h) = = 𝐒𝐢𝐧𝐀 𝑺𝒊𝒏𝑪 C 𝒉 ∠𝐂 = 𝟑𝟏 𝐒𝐢𝐧𝐛 𝑺𝒊𝒏𝑪 𝒔𝒊𝒏(𝟖𝟐) = 𝟓. 𝟕 𝐜 𝐒𝐢𝐧𝐀 𝐜 𝐒𝐢𝐧𝐁 𝐚 = 𝐛= 6.2 mi 5.7 mi 𝑺𝒊𝒏𝑪 𝑺𝒊𝒏𝑪 𝐡 = 𝟓. 𝟕 ∙ 𝐒𝐢𝐧(𝟖𝟐) h A 67o 𝐚 = 𝟓.𝟕 𝐦𝐢 82o 3.2 mi B Formula Sheet 𝐛 = 𝟔.𝟐 𝐦𝐢 𝐡 = 𝟓. 𝟔 𝒎𝒊