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tino4ka555 [31]
3 years ago
7

How does the unit circle allow the trigonometric functions to be defined for all real numbers instead of just for acute angles?

Mathematics
1 answer:
Molodets [167]3 years ago
8 0

Every point in the unit circle is identified either by its coordinates (x,y) or by the angle it forms with the x-axis, \alpha.

The trigonometric functions associate with every angle \alpha and the correspondant (x,y) coordinates the two values

\cos(\alpha)=x,\quad\sin(\alpha)=y

This procedure can be done for every angle \alpha, so you don't have to work with acute angles only.

You might be interested in
Solve using a2 + b2 = c2 <br> show ur work please :)
Brrunno [24]
So 90^2+90^2=c^2
8100+8100=c^2
16200=c^2
C= ~127.28
5 0
3 years ago
I need help, and I’m also confused.
amid [387]
There are two triangles, a big triangle and a small triangle that is inside the big triangle. Because the base of the triangles are parallel to each other( indicated by the arrow), and the small triangle is perfectly inside the bigger triangle, the sides of the triangles are proportional.

It is know that the base of the small triangle is 3.5, and the hypotenuse of the small triangle is 7cm. it is also known that the the hypotenuse of the big triangle is (7+8)=15 and the base of the big triangle is unknown.

Since the triangles are proportional,
to find the base of the big triangle

base(big)/hypotenuse(big)=base(small)/hypotenuse(small)

Plug in the numbers


x/15=3.5/7
x/15=1/2
x=15/2
x=7.5

The length of the base of the big triangle is 7.5cm
8 0
3 years ago
John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What i
Inga [223]

Answer:

Skiing costs $30 per hour and Boating costs $51 per hour.

Step-by-step explanation:

Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.

<em><u>"John paid $222 for four hours of skiing and two hours boating":</u></em>

4x+2y=222

<em><u>"He paid $213 for two hours skiing and three hours boating":</u></em>

2x+3y=213

<em>Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y</em>. Work shown below.

2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51

Hence, y = 51

<em>Now, substituting this y value into the 1st equation and solving for x will give us the value of x.</em>

First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30

Hence, skiing costs $30 per hour and boating costs $51 per hour.

4 0
3 years ago
Help me pleaseeee 5^4z-13 = 125
elena-s [515]
Z= 138/625 or in decimal form it’s 0.2208
6 0
3 years ago
Nate made 8 loaves of bread on Monday and 10 more on Tuesday. He gave an equal number to each of his 9 neighbors. How many loave
mars1129 [50]

Answer:

2

Step-by-step explanation:

8 + 10 = 18

18/9 = 2

8 0
3 years ago
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