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Nana76 [90]
3 years ago
8

Can someone help me with this? sin150° =

Mathematics
2 answers:
ElenaW [278]3 years ago
8 0

ANSWER

\sin(150 \degree) =  \frac{1}{2}

EXPLANATION

The principal angle for 150° is 30°.

The terminal side of 150° is in the second quadrant.

In this quadrant the sine ratio is positive.

This implies that;

\sin(150 \degree)= \sin(30 \degree)

On the unit circle,

\sin(30 \degree)   =  \frac{ 1 }{2}

Therefore

\sin(150 \degree)= \sin(30 \degree)   =  \frac{1 }{2}

marusya05 [52]3 years ago
6 0

Answer:

sin(150°) = 1/2

Step-by-step explanation:

* Lets study how we can solve this problem

- At first the measure of the angle is 150°

- Ask your self in which quadrant can you find this measure

* To know the answer lets revise the four quadrants

# First quadrant the measure of all angles is between 0° and 90°

  the measure of any angle is α

∴ All the angles are acute

∴ All the trigonometry functions of α are positive

# Second quadrant the measure of all angles is between 90° and 180°

  the measure of any angle is 180° - α

∴ All the angles are obtuse

∴ The value of sin(180° - α) only is positive ⇒ sin(180° - α) = sinα

# Third quadrant the measure of all angles is between 180° and 270°

  the measure of any angle is 180° + α

∴ All the angles are reflex

∴ The value of tan(180° + α) only is positive ⇒ tan(180° + α) = tanα

# Fourth quadrant the measure of all angles is between 270° and 360°

  the measure of any angle is 360° - α

∴ All the angles are reflex

∴ The value of cos(360° - α) only is positive ⇒ cos(360° - α) = cosα

* Now lets check the angle of measure 150

- It is an obtuse angle

∴ It is in the second quadrant

∴ the value of sin(150) is positive

∴ sin(150°) = sinα

∵ 180 - α = 150 ⇒ isolate α

∵ α = 180° - 150° = 30°

∴ sin(150°) = sin(30°)

∵ sin(30°) = 1/2

∴ sin(150°) = 1/2

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