Let theta be and angle in quadrant IV that has reference pi/3. What is sin(theta)?

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03-05-2021
Mathematics

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Let theta be and angle in quadrant IV that has reference pi/3. What is sin(theta)?

Sagot :

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erinna erinna · Answer 1 · 2021-05-09T21:31:39-04:00

Given:

[tex]\theta[/tex] is an angle in quadrant IV that has reference [tex]\dfrac{\pi}{3}[/tex].

To find:

The value of [tex]\sin \theta[/tex].

Solution:

We know that only cos and sec are positive in quadrant IV and all other trigonometric ratios are negative in quadrant IV.

Since [tex]\theta[/tex] is an angle in quadrant IV that has reference [tex]\dfrac{\pi}{3}[/tex], therefore the value of [tex]\sin \theta[/tex] must be negative.

[tex]\sin \theta=-\sin \dfrac{\pi}{3}[/tex]

[tex]\sin \theta=-\dfrac{\sqrt{3}}{2}[/tex]

Therefore, the required value is [tex]\sin \theta=-\dfrac{\sqrt{3}}{2}[/tex].

Sagot :

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