Exercise 3 2 Zup - But sine is nega±ve in quadrant 4(x-is...

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Exercise 3.1 Zup 1. Find the exact value of: a. sin 300 ° = triangle is a 30-60-90 triangle in quad IV with the 60 degree angle vertex at the origin. the sides of a 30-60-90 degree triangle are in the ratio 1:2:sqrt(3) (short leg:hypotenuse:long leg) sin(300) = opposite/hypotenuse = (long leg)/ (hypotenuse) = -sqrt(3)/2 b. tan (405 ° ) (Hint: 405 ° = 360 ° + 45 ° ) = tan(405) = tan(360 + 45) tan(360 + 45) = (tan(360) + tan(45))/(1 - (tan(360) * tan(45))) tan(360 + 45) = (0 + 1)/(1 - 0) tan(360 + 45) = 1/1 c. cot ( 13 π 3 ¿ (Hint: 13 π 3 = 4 π + π 3 ) cot(13π/3) = cot(2π + π/3) = cot(π/3) = cos(π/3) / sin(π/3) = (1/2) / (√3/2) = 1/√3 2. If sin θ < 0 and tan θ < 0, then in which quadrant does θ lie? sin θ > 0 in quadrants 2 and 3 sec θ < 0 in quadrants 1 and 2 common quadrant is 2. So θ lies in quadrant two 3. Find the exact value of sin θ, if cos θ = 4 5 and θ lies in quadrant IV. Page 1
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Exercise 3.1 Zup In the right-triangle in the diagram, cos(θ) = adjacent side/ hypotenuse = 4/5 Opposite side = sqrt[5^2-4^2] = sqrt[25-16] = sqrt(9) = 3 --- Pyhogorean theorem Therefore, sin(θ) = 3/5
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Unformatted text preview: But sine is nega±ve in quadrant 4 (x-is nega±ve) Therefore, sin(θ) = -3/5 4. DeFne the following for a sinusoidal graph in general. a. Amplitude= The amplitude is the distance from the "res±ng" posi±on (otherwise known as the mean value or average value ) of the curve. b. Period = The period of sine and cosine equa±ons relates to how o²en the graph goes a full repe±±on around the unit circle. The period is how long it takes for sine or cosine to return to the same place. c. Phase Shi² = Phase shif is any change that occurs in the phase of one quan±ty, or in the phase di³erence between two or more quan±±es. 5. Given the func±on 3sin2 y x a. ´ind the amplitude. Can’t Fgure out how to # 5 & 6 b. ´ind the period. Page 2 y x 5-5 1-1 3-3 y x 5-5 1-1 3-3 Exercise 3.1 Zup i. Identfy The correcT graph from The following choices: ii. Page 3 y x 5-5 1-2 3-3 Exercise 3.1 Zup iii. 6. Determine the amplitude, period, and phase shif oF 2cos( 3) y x . Page 4...
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