Categories

## If sin theta = 2/3, which of the following are possible

Sin ø = opposite/hypotenuse = 2/3, cos ø = adjacent/hypotenuse = ?/3, tan ø = opposite/adjacent = 2/?, sec ø = 1/cos ø

to solve ?, Pythagorean theorem must be applied

Manipulating the equation to find the adjacent value = ?

adjacent = sqrt(hypotenuse^2 – opposite^2) = sqrt(9-4)

so cos ø = sqrt(5)/3, tan ø = 2/sqrt(5) and sec ø = 3/sqrt(5) since the value is positive the possible equivalent trigonometric function should be positive, the answer should be b

Categories

## If sin theta = -0.7660, which of the following represents an approximate value of tan theta, for 180 degrees

Since we do not know where the angle of 23 degrees is located, then we can find the remaining side using the Pythagorean theorem. This can be done because we know that we have a triangle with a right angle.

We have then:

From here, we clear the value of x.

We have then:

Then, the area of the triangle is given by:

Where,

b: base of the triangle

h: height of the triangle

Substituting values:

Note: Maybe the height of the triangle is 27.6 instead of 11.8. This will depend on where the angle of 23.8 is located.

But for the moment of looking for the area of the triangle, this is not relevant because the product of the base for the height is the same.

The approximate area of the triangle is:

Categories

## Let theta denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the Bob is m, then the tension in string is

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

Explanation:

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t²      (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the  equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

Categories

## Three trigonometric functions for a given angle are shown below. Cosecant theta equals 13/12 secant Theta equals -13/5, cotangent equals -5/12. Where are the coordinates of point (x,y) On the terminal ray of angle theta assuming that the values above not simplified ?

False

Step-by-step explanation:

Suposse that we are given a function f(x) and a constant value h.

1. Case:

If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.

2.Case:

If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.

3.Case:

If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.

4. Case:

If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.

For example:

If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.

Categories

## If p(x,y) is the point on the unit circle defined by real number theta, then csc theta= _____. a. x/y. b. y/x. c. 1/x. d. 1/y.

(\$30-\$20)/\$0.1 = number of texts needed

Why is the equation like this. Here is the explanation.

We first need to find the price difference between the two subscriptions, therefore we subtract the cheapest subscription price from the expensive.

\$30-\$20

We then divide that number by the price per text message and end up with the number of texts needed for the subscriptions to cost the same. (We add the parentheses because of the order of operations. We want to subtract first, therefore we need the parentheses)

(\$30-\$20)/\$0.1

Let’s calculate the individual steps

\$30-\$20 = \$10
\$10/\$0.1 = 100

The total number of messages they need to send for the subscriptions to cost the same is 100.