0
If sin(x) = four fifths, then cos(x) = three fifths.
Sin-1(0.8) = 53.13 degrees.
Cos(53.13) = 0.6.
There are many ways you could work this out. One of them is to use the relationship between the squares of the sine and cosine:
sin2(x) = 1 - cos2(x)
(4/5)2 = 1 - cos2(x)
16/25 = 1 - cos2(x)
-cos2(x) = - 1 + 16/25
cos2(x) = 1 - 16/25
cos2(x) = 9/25
cos(x) = ±3/5
You could also work it out using good ol' Pythagorean theorem:
Let:
a ≡ adjacent
o ≡ opposite
h ≡ hypotenuse
Then we know:
sine = o/h
cosine = a/h
h2 = a2 + o2
We already have our opposite and hypotenuse sides, as we're given those with the value of the sine. We need to work out the adjacent side then:
h2 = a2 + o2
∴ a2 = h2 - o2
∴ a = (h2 - o2)1/2
∴ a = (52 - 42)1/2
∴ a = (25 - 16)1/2
∴ a = 91/2
∴ a = ±3
And now that we have the length of the adjacent side, as well as the hypotenuse, we know the cosine of the angle as that is is the ratio between the two:
cosine = a/h
∴cosine = ±3/5
Still curious? Ask our experts.
Chat with our AI personalities
Ross
Judy
EzraAdd your answer:
Earn +20 pts
Find the y-intercept of the graph y equals sin x?
It is zero.
What is the sin 29 equals x divided by 10?
2.9
Sin2x equals cos3x find x?
0. sin 2x = cos 3x 1. sin 2x = sin (pi/2 - 3x) [because cos u = sin (pi/2 - u)] 2. [...]
Find the value of y if sin y equals cos 48?
y = arcsin( cos 48 ); arcsin may be seen as sin-1 on your calculator.
In which quardant are the terminal arms of the angle lie when sin thita is less then zero and cos thita is greater then zero?
The fourth Across the quadrants sin theta and cos theta vary: sin theta: + + - - cos theta: + - - + So for sin theta < 0, it's the third or fourth quadrant And for cos theta > 0 , it's the first or fourth quadrant. So for sin theta < 0 and cos theta > 0 it's the fourth quadrant
Sin A equals 0.3779 find the degree and how?
22.20366435 sin^-1(0.3779)
How do you solve 2 sin squared theta equals one fourth?
2 sin^2 theta = 1/4 sin^2 theta = 1/8 sin theta = sqrt(1/8) theta = arcsin(sqrt(1/8))
Find the y-intercept of the graph y equals sin x?
It is zero.
What is the sin 29 equals x divided by 10?
2.9
Find the amplitude and period of the functions and sketch their graphs y equals sin -x?
y = sin(-x)Amplitude = 1Period = 2 pi
Tan equals 0.3421 sin equals 3237 Which quadrant does it terminate?
Assuming sin equals 0.3237, the angle is in quadrant I.
Sin2x equals cos3x find x?
0. sin 2x = cos 3x 1. sin 2x = sin (pi/2 - 3x) [because cos u = sin (pi/2 - u)] 2. [...]
Find the value of y if sin y equals cos 48?
y = arcsin( cos 48 ); arcsin may be seen as sin-1 on your calculator.
How do i find length of AB in the triangleABC angleB equals 95 degrees angleC equals 24 degrees and line AC equals 17cm how do i find the length of AB?
By use of the sine rule: sin A / BC = sin B / AC = sin C / AB Angles B and C are known, as is length AC, so: sin B / AC = sin C / AB AB = AC x sin C / sin B AB = 17cm x sin 24 / sin 95 ~= 6.94cm The ratios for the sine rule can also be given the other way up: BC / sin A = AC / sin B = AB / sin C (I learnt the rule the first way.) Further, if r is the radius of the triangle's circumcircle, then: sin A / BC = 1/2r or BC / sin A = 2r
How do you find sin theta when tan theta equals one fourth?
I will note x instead of theta tan(x) = sin(x) / cos(x) = 1/4 sin(x) = cos(x)/4 = ±sqrt(1-sin2x)/4 as cos2x + sin2 x = 1 4 sin(x) = ±sqrt(1-sin2x) 16 sin2x = 1-sin2x 17 sin2x = 1 sin2x = 1/17 sin(x) = ±1/sqrt(17)
Find the derivative of y equals 3cosx?
y=3 cos(x) y' = -3 sin(x)
In a triangle ABC b equals 15 cm and c equals 25 cm and also angle B equals 32'15'Find the side a and other angles?
By the sine rule, sin(C)/c = sin(B)/b so sin(C) = 25/15*sin(32d15m) = 0.8894 so C = 62.8 deg or 117.2 deg. Therefore, A = 180 - (B+C) = 85.0 deg or 30.5 deg and then, using the sine rule again, a/sin(A) = b/sin(B) so a = sin(A)*b/sin(B) = 28 or a = 14.3
