If 0*<theta<360*, find all values of theta, 2sintheta = 5costheta?

1 Answer
Nghi N.
Jun 27, 2018

68^@20, 248^@2068∘20,248∘20

Explanation:

2sin theta - 5cos theta = 02sinθ−5cosθ=0
Divide both sides by cos thetacosθ
Condition: cos theta != 0, or theta != pi/2, and theta != (3pi)/2cosθ≠0,orθ≠π2,andθ≠3π2
2tan theta = 52tanθ=5
tan theta = 5/2tanθ=52
Calculator and unit circle give 2 solutions for thetaθ:
theta = 68^@20θ=68∘20, and
theta = 68.20 + 180 = 248^@20θ=68.20+180=248∘20

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