Answer:
θ = πk, 1.318+2πk, 4.965+2πk
Step-by-step explanation:
4sin(2θ) − 2sin(θ) = 0
8sin(θ)cos(θ) - 2sin(θ) = 0
2sin(θ)[4cos(θ)-1] = 0
2sin(θ) = 0
sin(θ) = 0
θ = πk
4cos(θ)-1 = 0
4cos(θ) = 1
cos(θ) = 1/4
θ ≈ 1.318+2πk, 4.965+2πk
Therefore, θ = πk, 1.318+2πk, 4.965+2πk
Answer:
An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions.
Step-by-step explanation:
Trigonometric functions are derived from ratios of certain sides of a right triangle in reference to an angle. The graph of which is a wave, with amplitude in the y-axis and angle in the x-axis. We will first define the sine function written as:
sin(θ)=oppositesidehypotenuse
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Let
y
=
s
i
n
(
θ
)
y=sin(θ)
Then inverse trigonometric function outputs an angle. However, we can set y to its original value via transitivity:
s
i
n
−
1
(
y
)
=
θ
s
i
n
−
1
(
o
p
p
o
s
i
t
e
s
i
d
e
h
y
p
o
t
e
n
u
s
e
)
=
θ
sin−1(y)=θsin−1(oppositesidehypotenuse)=θ
Thus we see, that the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
From the equilateral (60-60-60) triangle with all legs of length 1, we can view half the triangle, forming a 30-60-90 triangle, with the hypotenuse measuring 1, the short leg1/2<span>, and the long leg 3 2. Therefore, we have sin 30° = </span>1/2<span>, cos 30° = 3 2, sin 60° = 3 2 and cos 60° = </span>1/2<span>.
i hope this help</span>
m/s is meters per second.
1 minute = 60 seconds.
2.5 minutes x 60 seconds = 150 seconds total.
150 seconds x 3.4 meters per second = 510 meters total.
they are both increasing at the same rate
Hope Your Thanksgiving Went Well, Here's Some Help Cleaning Up
-TheKoolKid1O1
