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2 years ago

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

Mathematics

1 answer:

Lady_Fox [76]2 years ago

6 0

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°

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3 years ago

The area A of a sector of a circle is given by A=πr²s/360, where r is the radius of the circle and s is the angle measure(in deg

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3 years ago

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grandymaker [24]

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2 years ago

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jarptica [38.1K]

Answer with explanation:

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This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.

Integrating Factor

$=e^{\int \frac{1+4x^2}{8x} dx}\\\\e^{\log x^{\frac{1}{8}+\frac{x^2}{2}}\\\\=x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}$

Multiplying both sides by Integrating Factor

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When , x=1, gives , y=9.

Evaluate the value of C and substitute in the equation 1.

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SashulF [63]

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tan theta=opposite/adjacent
theta=80
opposite=h
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tan 80=h/75
h=75 tan 80
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