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TOPICS | CONCEPTS |
---|---|

Trigonometry Ratios | Pythagorean Theorem |

Unit Circle | Sine, Cosine, Tangent Functions |

Trigonometric Identities | Angle Measurements & Conversions |

Inverse Trigonometric Functions | Solving Trigonometric Equations |

Trigonometric Graphs | Applications in Real Life |

Angles and Units | Angles in Standard Position |

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**Q1:**. Determine the exact value of each trigonometric ratio. Rationalize all ratios. \text { d) } \cos \left(\frac{25 \pi}{6}\right) \text { b) } \tan \left(60^{\circ}\right) \text { c) } \cos \left(-\frac{5 \pi}{4}\right) \text { d) } \cot \left(-120^{\circ}\right)See Answer**Q2:**\text { Determile a negative co-terminal angle, in degrees, with } \theta=\frac{4 \pi}{5} \text {. }See Answer**Q3:**A sundial creates a shadow as the Earth rotates that allows us to tell time, as shown below. If the length of the shadow is 25 cm in length, determine how far the tip of the shadow travelled from 7 a.m. to 3 p.m., to the nearest tenth of a centimeter.[2] See Answer**Q4:**State the period of the function y= tan(5x) as an exact value.See Answer**Q5:**Question 1 Example 4.20. The angle of elevation of the top of a broadcasting tower is 50° from the point A and 60° from the point B. It is given that the points are 120 metres apart and that A is due north of the tower, and B is due east of the tower. Let O be the base of the tower. a) Draw a diagram to illustrate this information. b) By letting the height of the tower beh, show that: i) OA = h cot 50° ii) OB = h cot 60° c) Hence find the height of the broadcasting tower correct to two decimal places.See Answer**Q6:**Question 2 Example 4.21. Two boats P and Q, are sitting in the water such that they subtend an angle of 60° from a point C at the base of a cliff. The angle of elevation from P and Q to the top of the cliff, 10 metres above C are 20° and 30° respectively. a) Find the distance between: i) C and P. ii) C and Q. b) Deduce the distance between the two boats correct to the nearest metre.See Answer**Q7:**Question 3 Example 4.22. The angle of elevation from a boat at P to a point T, at the top of a vertical cliff is measured to be 30°. The boat sails 1000 metres to a second point Q, from which the angle of elevation to T is measured to be 45°. Let R be the point at the base of the cliff directly below 7 and let h be the height of this cliff. The bearings of R from P and Q are 050ºT and 310ºT respectively. a) Draw a diagram expressing all this information. b) Show that ZPRQ = 100°. 1000² c) Show that h²= 4+2√3 sin 10° d) Hence evaluate the height of the cliff correct to the nearest metre.See Answer**Q8:**1. Solve the following triangle. Round all side lengths and angles to 1 decimal place. Show full steps to receive process marks. Ⓒ F 3.1 m 5.2 m ESee Answer**Q9:**2. Determine the length of side AB to one decimal place. Show full steps to receive process marks. Ⓒ 78° A 81° 18 cm 46° 14 cmSee Answer**Q10:**3. Determine the EXACT value of cos45°(1 - sec30°) using your special triangles. Simplify fully. Show all work to receive process marks. ⒸSee Answer**Q11:**4. The boom of a crane can be moved so that its angle of inclination changes. In one location, close to some buildings and some overhead power cables, the minimum value of the angle of inclination is 30°, and the maximum value is 60°. If the boom is 10 m long, find the vertical displacement of the end of the boom when the angle of inclination increases from its minimum value to its maximum value. a) Express your answer in EXACT form using your special triangles. Show all work to receive process marks. Ⓒ b) Express your answer in approximate form, to the nearest tenth of a metre. УА 10 m 60° 30° vertical displacement Уг 10 m xSee Answer**Q12:**5. Given angle 0, where 0° ≤ 0 ≤ 360°, determine two possible values of 0, to the nearest degree, where the following ratio would be true. Sketch both principal angles and label them using a diagram. Ⓒ tane = -0.9598See Answer**Q13:**6. Determine the number of possible triangles that could be drawn with the given measures. Only determine the height when needed. Fill in the table with your information. DO NOT SOLVE.Ⓡ Measures Height Given APQR, LP = 114°, p = 16, q = 28 Given ADEF, LE = 53°, ƒ = 10.7, e = 7.1 Given AJKL, ZK = 44°, l = 13.6, k = 9.4 Given AXYZ, ZX = 137°, x = 18.5, y = 6.2 Given AABC, LB = 28°, c = 18, b = 11 Number of Possible TrianglesSee Answer**Q14:**7. The point P(-5, -12) lies on the terminal arm of an angle in standard position. Determine the trig ratios for sine, cose and cote. Then find to the nearest degree. Include a fully labeled diagram. Ⓒ +See Answer**Q15:**8. If cote = =³/4 find all possible ratios for sine and cose, where 0° ≤ 0 ≤ 360°. Include a diagram. Ⓒ +See Answer**Q16:**9. Prove the following identity. Ⓒ (1 cos²0)(1+tan²0) = tan²0See Answer**Q17:**10. A light in a park can illuminate effectively up to a distance of 100 m. A point on a bike path is 150 m from the light. The sight line to the light makes an angle of 23° with the bike path. What length of the bike path, to the nearest metre, is effectively illuminated by the light? Show all steps to receive process marks. 23° 150 m Bike PathSee Answer**Q18:**11. To measure the height, CD, of an inaccessible cliff, a surveyor recorded the data shown. Find the height of the cliff, to the nearest tenth of a metre. Ⓒ Show all steps to receive process marks. A 38° D 50 m 61° 72° BSee Answer**Q19:**1. Making Conjectures 1) Sketch the come with a very small angle, keeping in mind that the last height is constant. Describe the effect on the radio and height of the come b) the one with very large angle leping in mind that the last height is constant Describe the effect as the ads and height of the came Make a conceding which type of angle would create a larger volume utify your The the com referitSee Answer**Q20:**I thing Triery Categ 2) Nighting formed with the come by the height and the radhes. Use a trig function to write an equation and have the equation for to find the ads of the com b)ling the right triangle, write an equation to find the height of the coSee Answer

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