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MATH / Find the degree measure of the least positive angle θ for which

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find the degree measure of the least positive angle θ\theta for which tanθ=cos5∘cos20∘+cos35∘cos50∘−sin5∘sin20∘−sin35∘sin50∘sin5∘cos20∘−sin35∘cos50∘+cos5∘sin20∘−cos35∘sin50∘.\tan \theta = \frac{\cos 5^\circ \cos 20^\circ + \cos 35^\circ \cos 50^\circ - \sin 5^\circ \sin 20^\circ - \sin 35^\circ \sin 50^\circ}{\sin 5^\circ \cos 20^\circ - \sin 35^\circ \cos 50^\circ + \cos 5^\circ \sin 20^\circ - \cos 35^\circ \sin 50^\circ}.
Plain-text mathematical notation (without MathML)
Find the degree measure of the least positive angle θ for which
tanθ=(cos5^(∘)cos20^(∘)+cos35^(∘)cos50^(∘)−sin5^(∘)sin20^(∘)−sin35^(∘)sin50^(∘))/(sin5^(∘)cos20^(∘)−sin35^(∘)cos50^(∘)+cos5^(∘)sin20^(∘)−cos35^(∘)sin50^(∘)).
Original LaTeX notation
Find the degree measure of the least positive angle $\theta$ for which
\[\tan \theta = \frac{\cos 5^\circ \cos 20^\circ + \cos 35^\circ \cos 50^\circ - \sin 5^\circ \sin 20^\circ - \sin 35^\circ \sin 50^\circ}{\sin 5^\circ \cos 20^\circ - \sin 35^\circ \cos 50^\circ + \cos 5^\circ \sin 20^\circ - \cos 35^\circ \sin 50^\circ}.\]

level

Level 5

type

Precalculus

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Source and history

task_id
3de1a107-56e8-5ed6-8d97-1d99feddd698
task_key
precalculus--test--3de1a107-56e8-5ed6-8d97-1d99feddd698
task_revision_id
1
config / split
precalculus / test

Official source

initial import