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1 Pure Mathematics

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Question 38
a.

A robotic arm's angular position ϕ\phiϕ (in radians) is monitored over time. Solve, for −π<ϕ<π-\pi < \phi < \pi−π<ϕ<π, the equilibrium equation

5sin⁡(2ϕ+0.8)+3=0 5\sin(2\phi + 0.8) + 3 = 0 5sin(2ϕ+0.8)+3=0

giving your answers, in radians, to 2 decimal places.

[4]
b.

In a static analysis of a structural joint, the angle α\alphaα (in degrees) must satisfy the condition

5tan⁡αsin⁡α=11−4cos⁡α 5\tan \alpha \sin \alpha = 11 - 4\cos \alpha 5tanαsinα=11−4cosα

Solve this equation for 0∘<α<360∘0^\circ < \alpha < 360^\circ0∘<α<360∘, giving your answers, in degrees, to one decimal place.

[6]

1 Pure Mathematics Questions

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Question bank

1.1.3 Set theory language and symbols
1.1.4 Definition, domain and range of functions