Use the unit circle to find all values of thetabetween 0 and 2Ï€ for which sin(theta)=sqrt 3/2

1 answer:

5 0

Sin(theta)=√3/2, 0≤theta≤360
In a unit circle, sin is y/r, r is always positive, y is positive in the first and second quadrant only.
sin60=√3/2, sin120=√3/2
so theta is 60 or 120

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iren2701 [21]

Answer:

(4,-8) and (4, 12)

Step-by-step explanation:

The equation of the hyperbola given is:

$\frac{(y-2)^2}{64}-\frac{(x-4)^2}{36}=1$

The general form of this hyperbola would be:

$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

Thus, we can see that:

a^2 = 64

a = 8

and

b^2 = 36

b = 6

The distance from one focus to center is called "c", it goes by formula:

$c^2=a^2+b^2$

Let's find c:

$c^2=8^2 + 6 ^2\\c^2=100\\c=10$

This is a vertical hyperbola and the center is found from the x and y's on the numerator:

(y-2)^2 means y = 2

(x-4)^2 = x = 4

Center is (4, 2)

We go 10 units vertically up, so from y = 2 , ten units up makes it y = 12

x = 4 and y = 12

(4,12)

We go 10 units vertically down, so from y =2, ten units down makes it y = -8

x = 4 and y = -8

(4, -8)

<u>Foci coordinates:</u>

3 0

3 years ago

Read 2 more answers

Hensley earns $8.50 per hour at an amusement park. She received a 12% raise when she becomes a manager at the gift store. How mu

ICE Princess25 [194]

First, find 12% of $8.50.

12% of $8.50 = 12% * $8.50 = 0.12 * $8.50 = $1.02

The raise is $1.02 per hour.

$8.50 + $1.02 = $9.52

Hear new hourly earnings are $9.52/hour.

3 0

3 years ago

Does 4( − 11) = 15 − 4 have a solution , infinite or none?

QveST [7]

Answer:

The equation given has no solution.

Step-by-step explanation:

The equation given is:

$4( -11) = 15 -4$