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pantera1 [17]
3 years ago
13

Cos(-170°) = _____ -cos10° cos10° cos(-10°)

Mathematics
1 answer:
ikadub [295]3 years ago
4 0

<em>The right answer for:</em>

<em>cos(-170°) = _____</em>

<em>is:</em>

<em>-cos10°</em>

<h2>Explanation:</h2>

The cosine function is an even function, which means that for every point (x,y) on the graph of y=cos(x) then the point (-x,y) also lies on the graph of the function. In other words, we can write:

cos(-170^{\circ})=cos(170^{\circ})

But:

170^{\circ}=180^{\circ}-10^{\circ}

So:

cos(170^{\circ})=cos(180^{\circ}-10^{\circ})

By property:

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})}

<h2>Learn more:</h2>

Trigonometric functions: brainly.com/question/2680050

#LearnWithBrainly

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