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What is to be learned?

What is to be learned?. A formula connecting gradient and angle. Gradient & Angle. tan θ = opposite / adjacent = (y 2 -y 1 ) (x 2 -x 1 ) = m AB. B(x 2 ,y 2 ). Opposite. X. θ. θ. Adjacent. A(x 1 ,y 1 ). gradient of line = tangent of angle m = Tan. θ.

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What is to be learned?

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  1. What is to be learned? • A formula connecting gradient and angle

  2. Gradient & Angle tan θ = opposite/adjacent = (y2-y1) (x2-x1) = mAB B(x2,y2) Opposite X θ θ Adjacent A(x1,y1) gradient of line = tangent of angle m = Tan θ

  3. The line GH makes an angle of 34° with the X-axis. Find its gradient. mGH = tan34° = 0.67 m = Tan θ NB: line looks like H 34° X G

  4. The line CD makes an angle of 110° with the X-axis. Find its gradient. mCD = tan110° = -2.75 m = Tan θ NB: line looks like C 110° X D

  5. Gradients and Angles If a line makes an angle of θ with the positive direction of the X-axis m = Tan θ B θ X A

  6. The line GH makes an angle of 116.6° with the X-axis. Find its gradient. mGH = tan116.6° = -2. NB: line looks like H 116.6° X G

  7. P is (5, -2) and Q is (17,10). What angle does PQ make with the X-axis? tan θ = (y2-y1) (x2-x1) = (10 + 2) ( 17 - 5) = 12/12 = 1 θ = tan-1(1) = 45°. NB: line looks like Q  X P

  8. P is (5, -9) and Q is (7,7). What angle does PQ make with the X-axis? tan  = (y2-y1) (x2-x1) = (7 + 9) ( 7 - 5) = 16/2 = 8 θ = tan-1(8) = 83°. NB: line looks like Q  X P

  9. Tanx = -0.4 A S i ii Always put a positive number here a0 180 – a iv iii Tan-1(0.4) = 220 180 + a 360 - a T C +ve or –ve? Tan -ve in ii and iv x = 180 - 22 or 360-22 = 1580 = 3380

  10. Making sense of this!(1580 or 3380) M = -0.4 x θ θ = 1580 3380?

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