The angular displacement, $ϕ\phi$ , of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:

\sec \phi = 32 \sin \phi

Show that this equation can be expressed in the form $sin⁡2ϕ=k\sin 2\phi = k$ , where $k\,$ is a constant to be determined.

Hence, find the smallest positive value of $ϕ\phi$ , in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.

The angular displacement, $ϕ\phi$ , of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:

\sec \phi = 32 \sin \phi

Show that this equation can be expressed in the form $sin⁡2ϕ=k\sin 2\phi = k$ , where $k\,$ is a constant to be determined.

Hence, find the smallest positive value of $ϕ\phi$ , in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.

1.8 E: Trigonometry

Question 79

Markscheme

1.8 E: Trigonometry

Question 79

Markscheme

1.8 E: Trigonometry

Question 79

1.8 E: Trigonometry Questions

1.8 E: Trigonometry

Question 79

1.8 E: Trigonometry Questions