What is sin -1 (1/2) if the terminal side of 0 is located in quadrant 1

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°

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answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.