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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

There are 96 girls and 72 boys who want to participate in 6th grade intramurals.

Gekata [30.6K]

Answer:

i) 24

ii) 4 girls, 3 boys

Step-by-step explanation:

The GCF is 24

96= 24*4

72= 24*3

I hope this helps!

5 0

3 years ago

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If

pav-90 [236]

Answer:

Second option: One solution. Independent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation $y=-5x+1$ is:

$b=1$

Now we need to find the x-intercept. Substitute $y=0$ and solve for "x":

$0=-5x+1\\\\5x=1\\\\x=\frac{1}{5}=0.2$

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation $y=-2x-2$ is:

$b=-2$

Now we need to find the x-intercept. Substitute $y=0$ and solve for "x":

$0=-2x-2\\\\2x=-2\\\\x=\frac{-2}{2}=-1$

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent

4 0

2 years ago

What is 100:25 in lowest terms

Ray Of Light [21]

4: 1 because you could divide both sides of the ratio by 25

5 0

3 years ago

How many terms are there in 37,38,39,40...,437

aivan3 [116]

Answer:

There are 401 terms.

Step-by-step explanation:

The first term is 37 (subtract 36 to get 1st). The last term is 437 (subtract 36 to get 401st).

8 0

2 years ago

Read 2 more answers

Suppose triangle ABC is reflected over the x-axis. If the distance between point A and A’ is 14, what is the distance between th

andreyandreev [35.5K]

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

$d+d=14$

$2d=14$

$d=\dfrac{14}{2}$

$d=7$

Therefore, the correct option is 1.

7 0

2 years ago