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taurus [48]
3 years ago
11

Solve 4 sinx + 9 cosx=0 for 0° ​

Mathematics
1 answer:
jonny [76]3 years ago
7 0

4 sin(<em>x</em>) + 9 cos(<em>x</em>) = 0

4 sin(<em>x</em>) = -9 cos(<em>x</em>)

tan(<em>x</em>) = -9/4

<em>x</em> = arctan(-9/4) + <em>nπ</em> … … … (in radians)

or

<em>x</em> = arctan(-9/4) + 180<em>n</em> ° … … … (in degrees)

where <em>n</em> is any integer.

I'm guessing you're solving for <em>x</em> over some domain, probably 0° ≤ <em>x</em> < 360°. In that case, you would have two solutions for <em>n</em> = 1 and <em>n</em> = 2 of

<em>x</em> ≈ 113.96°   and   <em>x</em> ≈ 293.96°

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