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Pls help! TRIGONOMETRY​

Pls help! TRIGONOMETRY​-example-1
User Hikaru
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2 Answers

5 votes

Answer:

x = 150 degree

x = 210 degree

Explanation:

cos(x) = -cos(30) = -√3/2

x = 150 degree

x = 210 degree

User Nocturnal
by
7.6k points
4 votes

Answer:

θ = 150°, 210°

Explanation:

Given:


\cos \theta=- \cos 30^(\circ), \quad 0 < \theta < 360^(\circ)

We know from trigonometric values of special angles that :


\cos 30^(\circ)=(√(3))/(2)

and that 30° is in Quadrant I.

Therefore:


-\cos 30^(\circ)=-(√(3))/(2)


\begin{array} c\cline{1-2} \sf Quadrant &amp; \sf Reference \: Angle\\\cline{1-2} \rm I &amp; \theta\\\cline{1-2} \rm II &amp; 180^(\circ)-\theta \\\cline{1-2} \rm III &amp; \theta - 180^(\circ) \\\cline{1-2} \rm IV &amp; 360^(\circ) - \theta \\\cline{1-2} \end{array}

Cosine is negative In Quadrants II and III. Therefore, use the above table to find the reference angles of 30° that make the cosine of the angle negative:


\cos (180-30)^(\circ)=-(√(3))/(2) \implies \cos 150^(\circ)=-(√(3))/(2)

and:


\cos (30-180)^(\circ)=-(√(3))/(2) \implies \cos (-150^(\circ))=-(√(3))/(2)

Therefore, θ = 150° ± 360°n, -150° ± 360°n.

So the measure of θ in the given interval is 150° and 210°.

User Ggurov
by
9.1k points

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