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2 years ago

How do I solve this?

Mathematics

1 answer:

Sonbull [250]2 years ago

5 0

The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.

sec(x) = csc(x)

By definition of secant and cosecant,

1/cos(x) = 1/sin(x)

Multiply both sides by sin(x) :

sin(x)/cos(x) = sin(x)/sin(x)

As long as sin(x) ≠ 0, this reduces to

sin(x)/cos(x) = 1

By definition of tangent,

tan(x) = 1

Solve for x :

x = arctan(1) + nπ

x = π/4 + nπ

(where n is any integer)

In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of

x = π/4 or x = 5π/4

You might be interested in

Si elegimos un día de la semana al azar, ¿qué probabilidad hay de que sea fin de semana (ya sabemos que hay dos días…)?

irga5000 [103]

Answer:

La probabilidad que hay de que sea fin de semana es $\frac{2}{7}$

Step-by-step explanation:

La Probabilidad es la mayor o menor posibilidad de que ocurra un determinado suceso. En otras palabras, la probabilidad establece una relación entre el número de sucesos favorables y el número total de sucesos posibles. Entonces, la probabilidad de un suceso cualquiera A se define como el cociente entre el número de casos favorables (número de casos en los que puede ocurrir o no el suceso A) y el número total de casos posibles. Esta se denomina Ley de Laplace.

$P(A)=\frac{numero de casos favorables}{numero de casos posibles}$

En este caso:

número de casos favorables: 2 (cantidad de días del fin de semana)
número de casos posibles: 7 (cantidad de días totales en la semana)

Reemplazando:

P(A)= $\frac{2}{7}$

La probabilidad que hay de que sea fin de semana es $\frac{2}{7}$

3 0

3 years ago

Six and nineteen hundredths in expanded form

ella [17]

The answer to your question should be 6.19

5 0

3 years ago

Read 2 more answers

dale is driving to Miami. suppose that the distance (in miles) is a linear function of his total driving time (in minutes). dale

nexus9112 [7]

Considering there is a function (relationship) and that it is linear, the distance will change proportionally to time constantly. In other words, we are taking the speed to be constant throughout the journey.
If we let:
t = time (min's) driving
d = distance (miles) from destination
Then we can represent the above information as:
t = 40: d = 59
t = 52: d = 50
If we think of this as a graph, we can think of the x-axis representing time and the y-axis representing the distance to the destination. Being linear, the function will be a line, i.e. it will have a constant gradient. If you were plot the two points inferred from the information and connect the two dots, you will get a declining line (one with a negative gradient) representing the inversely proportional relationship or equally, the negative correlation between the time driving and the distance to the destination. The equation of this line will be the linear function that relates time and the distance to the destination. To find this linear function, we do as follows:

Find the gradient (m) of the line:
m = Δy/Δx
In this case, the x-values are t-values and our y-values are d-values, so:
Δy = Δd
= 50 - 59
= -9
Δx = Δt
= 52 - 40
= 12
m = -9/12 = -3/4
Note: m is equivalent to speed with units: d/t

Use formula to find function and rearrange to give it in the desired format:
y - y₁ = m(x - x₁)
d - 50 = -3/4(t - 52)
4d - 200 = -3t + 156
4d + 3t - 356 = 0

Let t = 70 to find d at the time:
4d + 3(70) - 356 = 0
4d + 210 - 356 = 0
4d - 146 = 0
4d = 146
d = 73/2 = 36.5 miles

So after 70 min's of driving, Dale will be 36.5 miles from his destination.

3 0

3 years ago

So 13 divided by 3 is 4 but where is the 4 coming from because 4 groups of 3 is 12 so 13 minus 12 is 1 so how dose the 4 make it

Crazy boy [7]

13/3= 4.25 because.....

13-12 is 1.

SO:

When you have your problem set up, you have 4, and then a 1 left over. You turn it into a fraction.

Make 4 and 1/4, then put it as a mixed number, 4 1/4

or you can keep dividing by adding a decimal then zeroes and keep solving until you get 4.25 which is equivalent to 4 1/4

3 0

2 years ago

Read 2 more answers

Place parentheses in each equation if needed to make each equation true.

aniked [119]

I hope you like the answer that i just gave you.

3 0

3 years ago

Read 2 more answers