# Math Help - Help me with this full trigonometric equation?

1. ## Help me with this full trigonometric equation?

The angle θ, is the angular displacement of a point on a crank mechanism. When the mechanism comes to rest, this point could be in four possible positions denoted by the angle θ. The equation modelling the mechanism is 3sec²θ = 7-4tanθ. Calculate the four positions refferred to when the crank is at rest

2. Originally Posted by lewuk09
The angle θ, is the angular displacement of a point on a crank mechanism. When the mechanism comes to rest, this point could be in four possible positions denoted by the angle θ. The equation modelling the mechanism is 3sec²θ = 7-4tanθ. Calculate the four positions refferred to when the crank is at rest
Hi

$3 \sec^2 \theta = 7-4 \tan \theta$

Using $\sec^2 \theta = 1+\tan^2 \theta$

$3 + 3 \tan^2 \theta = 7-4 \tan \theta$

$3 \tan^2 \theta + 4 \tan \theta - 4 = 0$

This is a second degree equation in $\tan \theta$ that I guess you are able to solve