Answer:
sin^-1 (1/2) = 30°
Step-by-step explanation:
* Lets explain how to find the trigonometry functions from the unit circle
- The unit circle is the circle whose radius is 1 unit
- It intersects the four axes at:
# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)
# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)
- The terminal of any angle intersect it at point (x , y) where x² + y² = 1
- If The angle between the terminal side and the x-axis is Ф , then
# The adjacent side of Ф = x
# The opposite side of the angle Ф = y
- In the problem the terminal side lies in the first quadrant
∴ all the trigonometry functions are positive
∵ sin Ф = opposite/hypotenuse
∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1
∴ sin Ф = 1/2 ÷ 1 = 1/2
- To find Ф use the inverse function sin^-1 Ф
∵ sin Ф = 1/2
∴ Ф = sin^-1 (1/2)
∴ Ф = 30°
* sin^-1 (1/2) = 30°
