The expression 3t + 15 can be used to approximate the height, in inches, of a tree t years

nalin [4]

$\cos^2x-\sin^2x=\cos2x=\dfrac{\sqrt3}2$

In the interval $[0,2\pi)$ , $\cos x$ takes on the value of $\dfrac{\sqrt3}2$ when $x=\pm\dfrac\pi3$ . In general, this happens for $x=\pm\dfrac\pi3+2n\pi$ where $n$ is any integer.

So, the solutions to this equation satisfy

$2x=\pm\dfrac\pi3+2n\pi$

or, dividing by 2,

$x=\pm\dfrac\pi6+n\pi$

for all integers $n$ .

7 0

3 years ago

Need help with special right triangles

hjlf

Step-by-step explanation:

For solving this, it's important to know basic trigonometric functions:

sin = opposite side / hypotenuse

cos = adjacent side / hypotenuse

tan = opposite side / adjacent side

It's also important to know that it is necessary to know their values for special right triangles and angles of 30°, 45° and 60°

1. We are given angle if 45° and its adjacent side of 13. We want to know the opposite side (x) and hypotenuse (y). So:

tan = opposite side / adjacent side

tan 45 = x / 13

1 = x / 13

x = 13

Remember that tangent of 45° angle is 1.

We found the opposite side to be also 13.

To find y we can use:

sin = opposite side / hypotenuse

sin 45 = 13 / y

(√2)/2 = 13 / y

y = 13√2

Important to remember, sin 45 and cos 45 are (√2)/2

2. We are given 45° angle and hypotenuse of 30. We need to find opposite side (x) and adjacent side (y).

sin = opposite side / hypotenuse

sin 45 = x / 30

(√2)/2 = x / 30

x = 15√2

Also:

cos = adjacent side / hypotenuse

cos 45 = y / 30

(√2)/2 = y / 30

y = 15√2

We can conclude that in the right triangle, when angle is 45°, opposite and adjacent sides are equal.

3. We are given angle of 60° and adjacent side of 3. We need to find opposite side (y) and hypotenuse (x).

cos = adjacent side / hypotenuse

cos 60° = 3 / x

1/2 = 3 / x

x = 6

Note that cos 60° equals 1/2.

sin = opposite side / hypotenuse

sin 60° = y / 6

(√3)/2 = y / 6

y = 3√3

Note that sin 60° equals (√3)/2.

4. We are given angle of 30° and hypotenuse of 34. We need to find opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 30° = y / 34

1/2 = y / 34

y = 17

Note that sin 30° equals to cos 60° equals 1/2.

cos = adjacent side / hypotenuse

cos 30° = x / 34

(√3)/2 = x / 34

x = 17√3

Remember that cos 30° equals to sin 60° which is (√3)/2.

5. We are given an angle of 45° and hypotenuse of 10√2. We need to find the opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 45° = y / 10√2

(√2)/2 = y / 10√2

y = 10

To save time, we already said that opposite and adjacent sides are equal in right triangle with 45° angle, so x = y = 10.

6. We are given angle of 60° and opposite side of 25√3. We need to find adjacent side (y) and hypotenuse (x).

sin = opposite side / hypotenuse

sin 60° = 25√3 / x

(√3)/2 = 25√3 / x

x = 50.

tan = opposite side / adjacent side

tan 60° = 25√3 / y

√3 = 25√3 / y

y = 25.

Remember that tangent of 60° angle is √3.

7. We are given angle of 45° and hypotenuse of 2√14. We need to find adjacent side (x) and opposite side (y).

cos = adjacent side / hypotenuse

cos 45° = x / 2√14

(√2)/2 = x / 2√14

x = √28

Again, adjacent and opposite sides are equal in 45° right triangle, so x = y = √28.

8. We are given an angle of 30° and an adjacent side of 24. We need to find the opposite side (y) and hypotenuse (x).

tan = opposite side / adjacent side

tan 30° = y / 24

(√3)/3 = y / 24

y = 8√3

sin = opposite side / hypotenuse

sin 30° = 8√3 / x

1/2 = 8√3 / x

x = 16√3

Note that tan = sin/cos, so tan 30° = sin 30° / cos 30°

tan 30° = 1/2 / (√3)/2 = (√3)/3

I'm showing you this, so you don't have to memorize tan for special angles, you can find it from sin and cos.

9. We are given an angle of 60° and hypotenuse of 22√3. We need to find the opposite side (y) and adjacent side (x).

sin = opposite side / hypotenuse

sin 60° = y / 22√3

(√3)/2 = y / 22√3

y = 33

cos = adjacent side / hypotenuse

cos 60° = x / 22√3

1/2 = x / 22√3

x = 11√3

10. We are given an angle of 30° and the opposite side of √6. We need to find the adjacent side (x) and hypotenuse (y).

sin = opposite side / hypotenuse

sin 30° = √6 / y

1/2 = √6 / y

y = 2√6

tan = opposite side / adjacent side

tan 30° = √6 / x

(√3)/3 = √6 / x

x = √18

11. We are given an angle of 45° and an adjacent side of √10. We need to find the opposite side (x) and hypotenuse (y).

In this triangle opposite and adjacent sides are equal (45° angle), so x = √10

sin = opposite side / hypotenuse

sin 45° = √10 / y

(√2)/2 = √10 / y

y = √20 = 2√5

12. We are given an angle of 60° and the opposite side of 4√21. We need to find the adjacent side (x) and hypotenuse (y).

sin = opposite side / hypotenuse

sin 60° = 4√21 / y

(√3)/2 = 4√21 / y

y = 8√7

tan = opposite side / adjacent side

tan 60° = 4√21 / x

√3 = 4√21 / x

x = 4√7

13. Now things get a little trickier. We are given an angle of 30° and the opposite side of 17. We need to find the adjacent side (x).

Note that, at the moment, we are only dealing with this smaller triangle.

tan = opposite side / adjacent side

tan 30° = 17 / x

(√3)/3 = 17 / x

x = 17√3

Now, note that hypotenuse of the smaller triangle is the same length as the side z (adjacent and opposite side of 45° angle)

With Pythagorean theorem, we can find the hypotenuse of the smaller triangle, which equals to z.

z = √(17^2 + (17√3)^2)

z = 34

And now, finally to find y (hypotenuse of bigger triangle). We are given 45° angle and adjacent side z (34).

cos = adjacent side / hypotenuse

cos 45° = 34 / y

(√2)/2 = 34 / y

y = 34√2

14. Photo added

6 0

3 years ago

Please choose any two and help me answer i will be very grateful and will mark you brainliest

ehidna [41]

Answer:

18 and 20, 4

Step-by-step explanation:

Math reasoning 1:

Set the first number as x and the other one as x+2 because it is a consecutive even number.

x+x+2=38

2x=36

x=18

18+2=20

The 2 consecutive numbers are 18 and 20

Problem solving 1:

Write out equation first, set the unknown number as x

5+x=9

x=4

4 0

4 years ago

Read 2 more answers

Solve the equation for g.

vagabundo [1.1K]

This was very complex, but I do believe the answer is g=1/2*pi*w^3*A
2
HAPPY NEW YEAR!
hope this helped

6 0

4 years ago

Can someone help me with this problem

Illusion [34]

${a }^{2} + {b}^{2} = {c}^{2}$

${1}^{2} + {x}^{2} = {2}^{2}$
${x}^{2} = {2}^{2} - {1}^{2}$
${x}^{2} = 3 \\ \\ x = \sqrt{3}$
$\sqrt{3} = 1.73$

7 0

3 years ago