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Calculate sin13pi3, cos33pi4 and sin101pi2SolutionWell ca.pdf

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Calculate sin13pi/3, cos33pi/4 and sin101pi/2 Solution We\'ll calculate sin13pi/3. We notice that we can write: 13pi/3 = pi/3 + 12pi/3 pi/3 + 12pi/3 = pi/3 + 4pi But 4pi = 2*2pi. We can substitute 2pi by 0, because 2pi and 0 are overlapping. So, sin 13pi/3 = sin (2*2pi + pi/3) sin (2*2pi + pi/3) = sin pi/3 sin13pi/3 = sin pi/3 = sqrt3/2 We\'ll calculate cos33pi/4. We notice that we can write: 33pi/4 = pi/4 + 32pi/4 pi/4 + 32pi/4 = pi/4 + 8pi But 8pi = 4*2pi We\'ll substitute 2pi by 0. 4*2pi = 4*0 = 0 cos33pi/4 = cos (pi/4 + 4*2pi) cos (pi/4 + 4*2pi) = cos pi/4 cos33pi/4 = cos pi/4 = sqrt2/2 We\'ll calculate sin 101pi/2. We notice that we can write: 101pi/2 = pi/2 + 100pi/2 pi/2 + 100pi/2 = pi/2 + 50 pi But 50pi = 25*2pi We\'ll substitute 2pi by 0. sin 101pi/2 = sin (pi/2 + 25*2pi) sin (pi/2 + 25*2pi) = sin pi/2 sin 101pi/2 = sin pi/2 = 1.

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Calculate sin13pi/3, cos33pi/4 and sin101pi/2 Solution We'll calculate sin13pi/3. We notice that we can write: 13pi/3 = pi/3 + 12pi/3 pi/3 + 12pi/3 = pi/3 + 4pi But 4pi = 2*2pi. We can substitute 2pi by 0, because 2pi and 0 are overlapping. So, sin 13pi/3 = sin (2*2pi + pi/3) sin (2*2pi + pi/3) = sin pi/3 sin13pi/3 = sin pi/3 = sqrt3/2 We'll calculate cos33pi/4. We notice that we can write: 33pi/4 = pi/4 + 32pi/4 pi/4 + 32pi/4 = pi/4 + 8pi But 8pi = 4*2pi We'll substitute 2pi by 0. 4*2pi = 4*0 = 0 cos33pi/4 = cos (pi/4 + 4*2pi) cos (pi/4 + 4*2pi) = cos pi/4 cos33pi/4 = cos pi/4 = sqrt2/2 We'll calculate sin 101pi/2. We notice that we can write: 101pi/2 = pi/2 + 100pi/2 pi/2 + 100pi/2 = pi/2 + 50 pi But 50pi = 25*2pi We'll substitute 2pi by 0. sin 101pi/2 = sin (pi/2 + 25*2pi) sin (pi/2 + 25*2pi) = sin pi/2 sin 101pi/2 = sin pi/2 = 1

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Calculate sin13pi3, cos33pi4 and sin101pi2SolutionWell ca.pdf

  • 1. Calculate sin13pi/3, cos33pi/4 and sin101pi/2 Solution We'll calculate sin13pi/3. We notice that we can write: 13pi/3 = pi/3 + 12pi/3 pi/3 + 12pi/3 = pi/3 + 4pi But 4pi = 2*2pi. We can substitute 2pi by 0, because 2pi and 0 are overlapping. So, sin 13pi/3 = sin (2*2pi + pi/3) sin (2*2pi + pi/3) = sin pi/3 sin13pi/3 = sin pi/3 = sqrt3/2 We'll calculate cos33pi/4. We notice that we can write: 33pi/4 = pi/4 + 32pi/4 pi/4 + 32pi/4 = pi/4 + 8pi But 8pi = 4*2pi We'll substitute 2pi by 0. 4*2pi = 4*0 = 0 cos33pi/4 = cos (pi/4 + 4*2pi) cos (pi/4 + 4*2pi) = cos pi/4 cos33pi/4 = cos pi/4 = sqrt2/2 We'll calculate sin 101pi/2. We notice that we can write: 101pi/2 = pi/2 + 100pi/2 pi/2 + 100pi/2 = pi/2 + 50 pi But 50pi = 25*2pi We'll substitute 2pi by 0. sin 101pi/2 = sin (pi/2 + 25*2pi) sin (pi/2 + 25*2pi) = sin pi/2 sin 101pi/2 = sin pi/2 = 1