SOLVE FOR X:!!!!!!!!!!!!!!!!!!!

Question

cos(2x+10)=-sin76

Answer 1

cos(2x+10) = -sin76

Recall:  -sinθ = cos(90+θ) so, -sin76 = cos(90+76) = cos(166)

There fore  -sin76 = cos(166)

cos(2x+10) = cos (166)

Cancel common terms.

(2x + 10) = 166

Subtract 10 from each side.

2x + 10 - 10 = 166 - 10

2x = 156

Divide each side by 2.

x = 78

There fore x = 78.

Comments

Thank you!!!

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cos(2x + 10) = cos(166)

The genaral solution of cos(x) = cos(α) is x = 360n ± α, where n is an integer.

2x + 10 = 360n ± 166

2x + 10 = 360n + 166 and 2x + 10 = 360n - 166

2x = 360n + 156 and 2x = 360n - 176

x = 180n + 78 and x = 180n - 88.

So, the general solution is x = 180n + 78 and x = 180n - 88, where n ∈ Z.