Answer all questions please

Special Angles Special triangles can be used to determine the exact values of the primary and reciprocal trigonometric ratios for some angles measured in Triangle #1: 450, 450, 90 Triangle #2: 30, 60, 90 Square of side length 1: Equilateral triangle of side length 2: Trig ratios: Trig ratios: Unit 5: Trigonomet Date: Example 1: Determine the exact value (without a calculator) of the following a) (sin- )(cos )+ (sir (sin ")cos ) b) tan ? -sin? Angles on the Cartesian Plane We can represent any point P(x, y) on the Cartesian plane by measuring the radial distance of the point from the origin (r). and the angle formed between the positive x-axis and the point(0). The coordinates (r, 0) are the Polar representation of the point (x, y). The point P(x, y) lies on what is known as the Terminal arm . 0 is known as the principle angle and is always measured from P ( xy ) the positive x-axis in a counter clockwise direction (if 027) Related acute angle( B ): is the angle formed by the x-axis and the terminal arm. It is always less than 90. Every @ has a corresponding / ! Example 2: Convert the following point to their corresponding polar coordinates. a) P(1, v3) b) P (-V3 ,-1) Unit 5: Trigonometric Functions Date:_ Primary Trig Ratios in the Cartesian plane State the three primary trig ratios in terms or x, y and r. Which trig ratios are positive in the four quadrants? Example 3: Without a calculator, determine if the following ratios are positiveegative. a) tan b) cos- c) sin d)sec- 37t Example 4: Determine the exact value of a) sin Success Criteria: 1. Sketch the angle in standard position. Determine the related acute 3. Compare the related acute angle to the special triangles and determine the value nometric ratio. Refer to CAST to determine the sign of the ratio. c) tan d) sin e) sec Unit 5: Trigonometric Functions Date: Minds On: How many values of @ are possible when solving for sin 0 = _. where O S O S 27 ? Success Criteria: 1. Determine the first angle by taking the inv special triangles for exact values) and draw it. 2. Draw in the second angle that will also satisfy the equation using the CAST rule. Remember: there will always be two related acute angles that satisfy the equation. 3. Using the diagram, state the two measure(s) of 0. ensuring OSOS 2n . Example 5: Determine all values of @ such that 0 S @ $ 2 for a) cose = = b) sin 0 = _ V3 c) tan 0 = d) sece =-V2 e) cose =-0.62 () sin 9 =0. Unit 5: Trigonometric Functions Date: Lesson #2 - Practice: Radian Measure and Angles on the Cartesian Plane 1. Convert the following Cartesian coordinates to their Polar form a) P(3,3 b) P(-2,4) c) P(0,-5) d) P(1.- 13 ) 2. Without a calculator determine if the values of the following are negative/ positive or 0. a) tan b) cost c) cscat d) sec e) sing f) sec's 3. State the exact value of each: (No calculator) a) cos 4 b) sin c) cot d) cos's e) cos () sin g) sec h) tan ) sin 24 1) cso(- 3) k) Cos27 )tan $ 4. Without a calculator find all @ such that 0 S O S 27 a) sin 0 = b) tan 0 = -1 c) sec0 =- d) cose =0 e) cote = v3 f) cos 0 = - g) sin 0 =0 h) tane = i) csco =-1 5. Without a calculator find the value of each of the following: a) sin + sin + b) cosy - cost c) cos2 + cos0 6. Find the exact value of the unknown side indicated in the diagram below. ANSWERS: 1.a) (3 2. ") b)(4.47,2.03Rad) c) (5. = ) d) (2, 10r) 2a) - b)- c) + d) + e)- 1)- 3.a) - b) - # c)-1 d) 0 e) 2 01 9) v2 h) - 3 1) - 4 1) - 2 k) 1 1 53 4. a) 4. " b) 4, 4 c) .4x ") 4. 4 0) . 4 0 4. 4 9) 0, m, 2 h) 3, 45 1) 4 5. 8) 0 b) 1 c) 2 6. V13