hectictar

cos B = 0.7658          Take the inverse cosine of both sides.

arccos( cos B ) = arccos( 0.7658 )

B = arccos( 0.7658 )

B ≈ 40º

Since the trigonometric functions are based on a unit circle,

it can't tell you what the arcsin of 35.4 is.

You can only take the arcsin of a value between -1 and 1 (including -1 and 1).

I don't know the answer to that one....but the REAL question is:

What is the beer root...of a square ?                  

Haha! I do my fair share of dumb things too! But thanks 

First let's find what x values make the expression equal to zero.

2x² - x - 1 = 0

Divide through by 2.

x² - (1/2)x - (1/2) = 0

What two numbers add to -1/2   and   multiply to -1/2   ? →  -1 and 1/2

So we can factor this

(x - 1)(x + 1/2) = 0

Set each factor equal to zero and solve for x.

x - 1 = 0          x + 1/2 = 0

x = 1               x = -1/2

So, the interval that makes the expression less than zero will be

either     ( - ∞ , -1/2 ) \(\cup\) ( 1 , ∞ )     or     ( -1/2 , 1 )

Test a point in the first interval, say -1 .

2(-1)² - (-1) - 1 < 0

2 < 0     false

Test a point in the second interval, say 0 .

2(0)² - 0 - 1 < 0

-1 < 0     true

So, the x-values which make the expression less than zero must be in the interval ( -1/2 , 1 )

Wow! Thank you Guest, I sure do appreciate that! 

sin θ = opposite / hypotenuse

sin θ = 75 / 115

θ = arcsin( 75 / 115 )

θ ≈ 41º

Let's let the base of this triangle be 15 cm, and the height be the skinny purple line.

sin θ = opposite / hypotenuse

sin 48º    = height / 6

6 sin 48º = height

area = (1/2)(base)(height)

area = (1/2)(15)(6 sin 48º)

area ≈ 33.44 cm²

\(\large{\frac{3r^3}{2r} \\~\\ =\frac{3\,\cdot\, r\,\cdot\, r\,\cdot\, r}{2\,\cdot\, r}}\)

We can reduce the numerator and denominator by r ...(....and say r ≠ 0 ) .

\(\large{=\frac{3\,\cdot\, r\,\cdot\, r}{2} \\~\\ =\frac{3r^2}{2}}\)

Which is what you had !!