The intensity $I\,$ of a laser beam passing through a specific optical filter is modeled by the equation $5\cos^2 \alpha + \sin 2\alpha$ , where $\alpha\,$ is the angle of incidence.

Given that $I = 2$ , show that

2\tan^2 \alpha - 2\tan \alpha - 3 = 0

Hence, find all possible values of $\alpha\,$ in the range $\alpha < 2\pi\,$ for which the intensity is 2 units. Give your answers to two decimal places.

Determine the values of $x\,$ in the interval $0<x<π3\displaystyle 0 < x < \frac{\pi}{3}$ such that

5\cos^2 \left( 3x + \frac{\pi}{4} \right) + \sin \left( 6x + \frac{\pi}{2} \right) = 2

Give your answers to one decimal place.

The intensity $I\,$ of a laser beam passing through a specific optical filter is modeled by the equation $5\cos^2 \alpha + \sin 2\alpha$ , where $\alpha\,$ is the angle of incidence.

Given that $I = 2$ , show that

2\tan^2 \alpha - 2\tan \alpha - 3 = 0

Hence, find all possible values of $\alpha\,$ in the range $\alpha < 2\pi\,$ for which the intensity is 2 units. Give your answers to two decimal places.

Determine the values of $x\,$ in the interval $0<x<π3\displaystyle 0 < x < \frac{\pi}{3}$ such that

5\cos^2 \left( 3x + \frac{\pi}{4} \right) + \sin \left( 6x + \frac{\pi}{2} \right) = 2

Give your answers to one decimal place.

1.4 Trigonometry

Question 25

Markscheme

1.4 Trigonometry

Question 25

Markscheme

1.4 Trigonometry

Question 25

1.4 Trigonometry Questions

1.4 Trigonometry

Question 25

1.4 Trigonometry Questions