Question

Pls solve and explain
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Answer 1

`\theta = 60; \theta \approx 83; \theta \approx 277; \theta = 300`

Note that the approximate value you should calculate properly with the inverse cosine function of your calculator to the number of digits you want.

Explanation:

you already have a cosine. You might as well change that sine in a cosine too:

`8(1-cos^2\theta) +6cos\theta-9=0\\8cos^2\theta -6cos\theta+1 =0`

(note that in the second line I also switched every sign by multiplying by -1 just to have a positive lead coefficient - just a pet peeve of mine. Now replace
`x=cos\theta` and let's solve

`8x^2-6x+1=0\\\frac\Delta4 = 9-8 = 1\\x=\frac {3\pm1}8`

At this point we're back to the replacement. We have two options

`cos\theta = \frac48 = \frac 12 \implies \theta = 60\°; \theta = 300\°\\cos\theta =\frac 18 \implies \theta \approx 83\°; \theta \approx 277\°`