Solved: "How to solve 2cos⁡150°−3sin⁡90°+tan⁡210°"

Khaleesi Herbert

Answered question

2020-10-27

How to solve

2 \cos 150 ° - 3 \sin 90 ° + \tan 210 °

unessodopunsep

Skilled2020-10-28Added 105 answers

To find the related angles of given ones, and their (+) or (-) signs, use the unit circle.

\cos 150 ° = \cos (180 ° - 30 °) = - \cos 30 ° = - \frac{\sqrt{3}}{2} (30 ° - 60 ° - 90 °, or 1 - 2 - \sqrt{3} △), \sin 90 ° = 1

, and

\tan 210 ° = \tan (180 ° + 30 °) = \tan 30 ° = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}

(30°-60°-90° triangle)
The given equation is restated as follows:

2 \cos 150 ° - 3 \sin 90 ° + \tan 210 ° = - 2 \cos 30 ° - 3 \sin 90 ° + \tan 30 °

= - 2 \frac{\sqrt{3}}{2} - 3 (1) + \frac{\sqrt{3}}{3} = - \frac{9 + 2 \sqrt{3}}{3}

(= approx. -4.1547)

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