**PLEASE HELP I NEED IT WITHIN 20 MINUTES**

These are Trig Ratios and you can read the instructions to solve question 15 & 16 (if you can please show the work it would be greatly appreciated)

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.

The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]

The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).

Contents

Right-angled triangle definitions Edit

A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.

Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.

If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]

sine

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Calculate 8/9-2/3 giving your answer in its simplest form.

' the length of one side of an equilateral is 3x+2. its perimeter is 60 centimeters. write an equation that could be used to find the value of x. solve for x and then find the length of the side. ''
I need to find the equation and the side length :')
also please answer this quickly hhhhhhhhhhhhh

WHO LIKES LARRAY
Cause I do

If x=5 and the area of the rectangle is 30 what is the other length of the rectangle?

Combine like terms to write a simplified expression:

12p + 11 - 5p + 3

The cheerleaders at City High make their own
megaphones by cutting off the small end of a
cone made from heavy paper. If the small end of
the megaphone is to have a radius of 2.5 cm,
what should be the height of the cone that is cut
off?
2.5 cm
60 cm​

Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!

hellppppp please simplify the expression- 96

Write an equation in Slope Intercept form with a slope of -5 and y-intercept of 4. (No spaces)​

if triangle GHI is equilateral and JHK is isosceles, what is the measure of JHK

ASAP When 4(0.5x+2.5y-0.7x-1.3y+4) is simplified, what is the resulting expression?

A) -0.8x+4.8y+16

B) 0.8x-4.8y+16

C) -0.8x-4.8y+4

D) 0.8x+4.8y+4

A train leaves LA at 2:00 pm and heads north at 50 mph. If the next train leaves the station three hours later and heads north at 60 mph, at what time will the second train catch up to the first train?

kate ran 4 miles how far did she run in kilometers

Factor completely: 125 x cubed space plus space 343

Please help me i will give brainlist please...

35x-12= -34x+710 answer fast too

3 +5.2.c = 1 - 2.87

ILL MARK BRAINLIEST IF FAST
Select the correct answer.
Which table represents a linear function that has a greater unit rate than that of the function y = 200x + 50?

first to answer correctly gets brainleist! (bringing out a lot of questions so yea!)

This table represents a linear function. Find the missing values to complete the table.

PLEASE HELP WILL GIVE BRAINLIEST

HELP ASAP PLEASE !!!><
WILL GIVE BRAINLIEST ❤️


Find the slope of the line passing through the given points using the slope formula. Describe the slope as
positive, negative, zero, or undefined.
(-5, -18) and (-5, -3)

Sup nerds. Do this for me or I'm gonna get screamed at by my mom also show all the work

jackson usually makes $250 per week working at a grocery store. Last week he made 60% more than usual. This week Jackson hopes to make 7/8 of what he made last week. how much money does jackson hope to make this week?

what are the x and y intercepts of the function f(x)=x/x^2-3x​

You are saving for a bike and can save $10 per week. You have $25 when you begin saving. Write an explicit equation
to represent the amount of money you have saved at any given week.

why cant anyone answer my long math question that has 70 or 60 points on it, come on guys.

steve saw 313 birds during a bird-watching trip to Yellowstone National park. he observes 15 more trumpeter swans than sandhill cranes. he saw twice as many mountain chickadees as ducky grouses. how many birds of each type did steve observe if he saw half as many trumpeter swans as ducky grouses

NEED ASAP!

Thomas has a bag with 6 purple and 5 blue marbles. If his friend Nick pulls 2 marbles from the bag, what is the probability of him getting 2 purple marbles. 30/121 30/121 21/22 21/22 3/11 3/11 11/21

two common multiples of 4 and 8 are​