The right answer for:
cos(-170°) = _____
is:
-cos10°
The cosine function is an even function, which means that for every point [tex](x,y)[/tex] on the graph of [tex]y=cos(x)[/tex] then the point [tex](-x,y)[/tex] also lies on the graph of the function. In other words, we can write:
[tex]cos(-170^{\circ})=cos(170^{\circ})[/tex]
But:
[tex]170^{\circ}=180^{\circ}-10^{\circ}[/tex]
So:
[tex]cos(170^{\circ})=cos(180^{\circ}-10^{\circ})[/tex]
By property:
[tex]cos(a-b)=cosacosb+sinasinb \\ \\ a=180^{\circ} \\ \\ b=10^{\circ} \\ \\ cos(170^{\circ} )=cos(180^{\circ} -10^{\circ})=cos180^{\circ} cos10^{\circ} +sin180^{\circ} sin10^{\circ} \\ \\ cos(170^{\circ})=-cos(10^{\circ})+0 \\ \\ \boxed{cos(170^{\circ})=-cos(10^{\circ})}[/tex]
Trigonometric functions: https://brainly.com/question/2680050
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