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
ANSWER
[tex]\sin(150 \degree) = \frac{1}{2} [/tex]
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;
[tex] \sin(150 \degree)= \sin(30 \degree) [/tex]
On the unit circle,
[tex] \sin(30 \degree) = \frac{ 1 }{2} [/tex]
Therefore
[tex]\sin(150 \degree)= \sin(30 \degree) = \frac{1 }{2} [/tex]
