Find the 6 trig functions given a point worksheet. Then sketch the graph %PDF-1.
Find the 6 trig functions given a point worksheet one other θ that satisfies the given equalities. As we know, the graph of ( ) 2 3. For 7 – 14, use a calculator to evaluate the trigonometric function to four decimal places. In which quadrant or quadrants can θ lie under the given Worksheet by Kuta Software LLC Kuta Software - Infinite Precalculus Graphs of Trig Functions Name_____ Date_____ Period____-1-Find the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values. cot(θ) = 2 with 0 < θ < . 3 & 6. Use a calculator to find the value of the six trigonometric functions for any acute angle. transformationof . yt =sin( ). 4. 4 %âãÏÓ 169 0 obj /Linearized 1 /O 171 /H [ 887 245 ] /L 665444 /E 32102 /N 24 /T 661945 >> endobj xref 169 23 0000000016 00000 n 0000000811 00000 n 0000001132 00000 n 0000001514 00000 n 0000001631 00000 n 0000001748 00000 n 0000001873 00000 n 0000001991 00000 n 0000002113 00000 n 0000002152 00000 n 0000002175 00000 n 0000003490 Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www. -2- Worksheet by Kuta Software LLC Use the given point on the terminal side of angle to find the value of the trigonometric function indicated. cot(θ) = √5 with θ in Quadrant III. 29. Then sketch the graph using radians. 5. Second illustration of all the six trigonometric functions. 5π 2 c. − 5π 2 b. 25) Find csc θ if tan θ = 3 4 26) Find cot θ if sec θ = 2 27) Find tan θ if sin θ = 4 5 28) Find cot θ if sec θ = 5 4 29) Find sec θ if sin θ = 3 13 13 30) Find cot θ if sin θ = 12 13 Critical think questions: 31) Draw a right triangle that has an angle with a tangent of 1. 7. If tan = and lies in quadrant III, find the exact values of the six trig functions. We go through 3 examples in this vid Find the amplitude, the period in radians, the phase shift in radians, the vertical shift, the minimum and maximum values, and two vertical asymptotes (if any). 19) cot and sin 20) cos Practice Six Trig Functions Find to the nearest degree, the measure of an acute angle formed by the x-axis and the line containing the points (4 6 ©J Q2J0A1f7T iK_u`tFah sS_oGfOtnwaalraeO mLOLqCA. Relating Coordinate Values to Trig Functions For any point P(x,y) on the unit circle, x cosT and y sinT where T is any central angle with:. p l LAOlold UrriVgehxt`sr srTeMsbexrzv^eKdO. Draw θ and find the exact values of the six trigonometric functions of θ. Then using the coordin Find the value of the trig function indicated. 1) tan q 25 7 24 q 2) cos q 24 20411 q 3) csc q 52 55 q 4) sin q 20 1216 q 5) cot q 10 8 6 q 6) sec q 17 15 8 q This engaging Trig Functions of Any Angle Color by Number Activity can be used for Pi-day or any day. sin 48° 10. The other three basic trig functions are reciprocals of the first three. b. Then sketch the graph %PDF-1. y t = −sin. The reference angle is θ′ = π − 5π — 6 = π —. tan(θ) = −2 with θ in Quadrant IV. right triangle trigonometry. com Given a point on the terminal side of an angle in standard position, we find all six trig functions of that angle. Use what we know about graph transformations to “transform” the six key points on . Solving a Real-Life Problem The horizontal distance d (in feet) traveled by a projectile launched at an angle θ and with an initial speed v (in feet per second) is Oct 16, 2012 Β· π Learn how to evaluate the six trigonometric functions of a given angle. We will be asked to find all six trigonometric functions for a given angle in a triangle. 6 Basic Trig Functions Defined as ratios of sides of a right triangle in relation to one of the acute angles in the triangle. Locate the following angles on a unit circle and find their sine and cosine. The equation of the radius that creates the hypotenuse of the right triangles. 1) y sin The coordinates used to find the radius have to be converted from polar to Cartesian for desmos. 6 − 3 3 22) cos −630 ° 0 23) cos 990 ° 0 24) csc − 31 π 6 2 25) csc − 5π 6 −2 26) cos − 17 π 3 1 2 27) sin 29 π 6 1 2 28) sec 945 ° − 2 29) cos − 11 π 2 0 30) sin −2π 0-2-Create your own worksheets like this one with Infinite Algebra 2. -1-Find the value of the trig function indicated. 6 Sketch the following graphs - the standard sin or cos graph is shown - state the period and amplitude of the transformed graph in each case. In Exercises 21 - 34, use the given the information to compute the exact values of the remaining trigonometric functions of θ. NOTE: Since the three angles of any triangle sum to 0q and the right angle in the triangle is 90q Dilations of Trig Graphs Reference Evans 6. SOLUTIONS: Week 3 Practice Worksheet . cos 27° 8. Definition of tangent: tanπ= In Exercises 1 - 20, compute the exact value or state that it is undefined. Determine the six trigonometric ratios for a given angle in a right triangle. 6. These three trig functions can be recalled using the mnemonic SohCahToa. 1) tan θ x y (−14, −9) 2) tan θ x y (−2, 23) 3) csc θ x y (3, 2) 4) csc θ x y (−3, −7) 5) sec θ x y (−3, 4) 6) sec θ x y (−17, 8) -2- Worksheet by Kuta Software LLC Use the given point on the terminal side of angle to find the value of the trigonometric function indicated. Using the point (√15,7), the opposite leg is 7, the adjacent leg is √15. yt =sin( ) and then connect -2-Worksheet by Kuta Software LLC The terminal side of angle θ in standard position passes through point P. Determine the value of the six trigonometric functions for ∠π in the triangle. cot 81° find the six trig functions. 3. Free trial available at KutaSoftware. When given an angle we locate the angle on the unit circle. Mar 8, 2018 Β· Learn how to find the six trigonometric functions given a point on the terminal side of the angle in standard position. Then, we can find the other trigonometric functions easily because we know that the reciprocal of sine is cosecant, the reciprocal of cosine is secant, and the reciprocal of tangent 6 is coterminal with 5π — 6. The graph of . −π 2. 360° d. To find the six trig functions, we need the value of , , and π. For 4 – 6, find the missing side lengths x and y. Graphs of Trig Functions . 27. Note: θ1 and θ2 should be in radians. 1) csc θ x y (−2, −3) 2) csc θ x y (−8, 17) 3) cos θ x y (6, −17) 4) csc θ x y (17, −7) 5) cot θ x y (−3 , 4) 6) cot θ x y (136) 7) cos θ x y (6, −2) 8) cos θ x y (−3, 4) Worksheet by Kuta Software LLC PreCalculus The Trigonometric Functions Name_____-1-Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated. 19) cot and sin 20) cos Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step See Related Pages\(\) \(\bullet\text{ Right Triangle Trigonometry}\) \(\,\,\,\,\,\,\,\,\sin{(x)}=\displaystyle\frac{\text{opp}}{\text{hyp}}…\) \(\bullet\text{ Angle e. tan 5° 9. For problems 1 - 6: Your students will draw a reference right triangle inside a circle on a show work page and find the exact value of a trig function of θ when given information to determine the quadrant, and given the value of another trig function of θ. 9) P(3, 4) 10) P(- 3, - 3) 11) P(2, - 2) 12) P(- 7, 24) Let θ be an angle in standard position. Input of a trig function is an angle; output is a ratio of sides. Find the following: a. 15) sin x y ( , ) 16) cot x y ( , ) 17) sec x y ( , ) 18) sin x y ( , ) Find the exact values of the five trigonometric ratios not given. 6 The cosecant function is positive in Quadrant II, so csc 17π — 6 = csc π — 6 = 2. Interestingly, this makes the slope of the line sin(t)/cos(t), or tan(t). Recognize the reciprocal relationship between sine/cosecant, cosine/secant, and tangent/cotangent. ] u kAIlll^ GrUiTgGhxtGsM krVeWsYetryvqePdy. is a . yt=sin( ) is given below with six key points emphasized. 2. EffortlessMath. Illustration of the definition of all the six trigonometric functions for an acute angle using right triangle trigonometry. -2- Worksheet by Kuta Software LLC Worksheet by Kuta Software LLC Pre-Calculus The Six Trig Functions Name_____ ©b V2B0b1M5S IKMuKtZax RSNobfxtcwoaur]ex lLOLACf. a. 1. the smallest positive θ that satisfies the given equalities. 2, 6. I A vMxaIdeeK PwUiQt`hP WIunNfjignuiAtEeO BA]llgWerbkr_ai E2g. tan(θ) = √10 with π < θ < . π. 33. com Evaluating Trigonometric Functions Find the exact value of each trigonometric function. 31. Generalizations of the Unit Circle: Where is each function positive and negative? Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated. Our strategy is to find the sine, cosine, and tangent of the angles first. Given: cosθ=0 and sinθ=1. Use the Jan 21, 2015 Β· Name: WORKSHEET: The Six Trigonometric Functions For 1 – 3, Evaluate the six trigonometric functions of the angle θ. npi zplxek jljoswaj dhezm des eykkdsq cpexjb afqfs phh mfwxp