Find the value for sin θ given the point (-3, 4) - id34634516, destinydiamond6887

Ответ:

rileyeddins1010

12.03.2022

Mathematics

sin θ = 4/5

Step-by-step explanation:

The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:

h² = (-3)² +(4)² = 25

h = 5 . . . . . . . . take the square root

The mnemonic SOH CAH TOA reminds you ...

Sin = Opposite/Hypotenuse

For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.

So, you have

sin θ = opposite/hypotenuse = 4/5

$Find the value for sin θ given the point (-3, 4) on the terminal side. leave your answer in fraction$

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Ответ:

moynihansavanah003

18.09.2021

Mathematics

$54\pi\ cm^2$

Step-by-step explanation:

1. Approach

In order to solve this problem, one needs to find the height of the cone. This can be done using the Pythagorean theorem. After finding the height of the cone, one can use the formula to find the surface area of a cone, to find the surface area of this particular cone.

2. Find the height of the cone

The Pythagorean theorem is a property that relates the sides of a right triangle. The radius (distance from the center to circumference (outer edge)) of the base, the height of the cone, and the slant of the cone forms a right triangle. Thus, one can use the Pythagorean theorem to solve for the height. The Pythagorean states the following:

a^2+b^2=c^2

Please note that (a) and (b) represent the sides adjacent (next to) the right angle, (c) represents the hypotenuse (the side opposite the right angle). In this case (a) is the height, and (b) is the radius of the base. (c) is the diagonal of the cone. Substitute the given values in and solve for the height,

a^2+b^2=c^2

a^2+3^3=15^2

Simplify,

a^2+3^3=15^2

a^2+9=225

Inverse operations,

a^2+9=225

a^2=216

$a=\sqrt{216}$

3. Find the surface area of the cone

The following formula can be used to find the surface area of a cone,

$A_s=\pi r(r+\sqrt{h^2+r^2})$

Where (h) is the height of the cone, (r) is the radius of the base of the cone, and ( $\pi$ ) represents the value (3.1415...). Substitute the given values into the formula and solve for the surface area,