If sin θ = 3/5, then cos θ = ?...Any ideas?
回答 (12)
2009-05-07 3:48 pm
✔ 最佳答案
remember that sin^2+cos^2=1
so you can say (3/5)^2+(x^2)=1
or
9/25 +x^2 =1
x^2=(16/25)
so x=(4/5)
so that's your answer :)
EDIT: don't use arc sin's and stuff. This way you can do it without a calculator possibly.
2009-05-07 3:52 pm
There are two solutions that you can have to solve this problem:
SOLUTION 1 ---
Use the basic trigonometric identity
sin^2 Θ + cos^2 Θ = 1
OR rearranging the above,
cos^2 Θ = 1 - sin^2 Θ
Substituting the value of sin Θ
cos^2 Θ = 1 - (3/5)^2
cos^2 Θ = 1 - 9/25 = 16/25
cos Θ = sqrt (19/25)
cos Θ = 4/5
SOLUTION 2 --
Since the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, then clearly the dimensions of this triangle would be:
Leg opposite the angle = 3
Hypotenuse = 5
and using the Pythagorean theorem, then
Leg adjacent to the angle = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt 16 = 4
and since the cosine of an angle is ratio of the length of the adjacent side to the length of the hypotenuse, then
cos Θ = 4/5
Hope this helps.
SOLUTION 1 ---
Use the basic trigonometric identity
sin^2 Θ + cos^2 Θ = 1
OR rearranging the above,
cos^2 Θ = 1 - sin^2 Θ
Substituting the value of sin Θ
cos^2 Θ = 1 - (3/5)^2
cos^2 Θ = 1 - 9/25 = 16/25
cos Θ = sqrt (19/25)
cos Θ = 4/5
SOLUTION 2 --
Since the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, then clearly the dimensions of this triangle would be:
Leg opposite the angle = 3
Hypotenuse = 5
and using the Pythagorean theorem, then
Leg adjacent to the angle = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt 16 = 4
and since the cosine of an angle is ratio of the length of the adjacent side to the length of the hypotenuse, then
cos Θ = 4/5
Hope this helps.
2009-05-07 3:50 pm
sin θ = 3/5
θ ~= 36.87
cos θ = 0.8 = 4/5
θ ~= 36.87
cos θ = 0.8 = 4/5
2009-05-07 3:49 pm
coh=4/5
cause it is a right triangle and the 3rd isde is 4 so that mean hyp. is 5 and thna the legs are 3 and 4. so look at SOHCAHTOA is sin is 3/5 than the cos is 4/5
cause it is a right triangle and the 3rd isde is 4 so that mean hyp. is 5 and thna the legs are 3 and 4. so look at SOHCAHTOA is sin is 3/5 than the cos is 4/5
2009-05-07 3:48 pm
Well, sin²θ + cos²θ = 1, so if sinθ = 3/5,
cos²θ = 1 - 9/25 = 16/25
So cosθ = ± 4/5.
cos²θ = 1 - 9/25 = 16/25
So cosθ = ± 4/5.
2009-05-07 3:48 pm
sin@ = opp/hyp
right?
so what triangle has a hypotenuse of 5 and a leg of 3?
why, a 3-4-5 triangle!
so it's 4/5
right?
so what triangle has a hypotenuse of 5 and a leg of 3?
why, a 3-4-5 triangle!
so it's 4/5
2016-05-28 3:35 am
I'm not sure about the sin theta <0 but given that cos theta=3/5...draw a triangle and find out the other side. use pythagorean thm: a^2+b^2=c^2 cos=adj/hyp=>a leg/hyp 3^2+b^2=5^2 9+b^2=25 b^2=16 so b=4 now we have all the sides of the triangle and we can use this to solve for the rest a) sin= - 4/5 b)sec=1/cos= 5/3 c)csc=1/sin= - 4/5 d)tan=sin/cos= - 4/3 e)cot=1/tan= - 3/4 Maybe the interval means that cos is in quad 4 because sin is less <0 so that means we change signs of anything but cosine and secant
2009-05-07 4:38 pm
sinθ = 3/5
(height = 3, hypotenuse = 5, base = ?)
a^2 + ?^2 = c^2
3^2 + ?^2 = 5^2
9 + ?^2 = 25
?^2 = 25 - 9
? = √16
? = 4
∴ cosθ = 4/5
(height = 3, hypotenuse = 5, base = ?)
a^2 + ?^2 = c^2
3^2 + ?^2 = 5^2
9 + ?^2 = 25
?^2 = 25 - 9
? = √16
? = 4
∴ cosθ = 4/5
2009-05-07 4:02 pm
sin θ = 3/5
......./|
....../.|
..5./..|
.../....|.3
../___|
.....4
we use the pethagorean theorem to solve for adjacent
c^2=a^2+b^2
a^2=c^2-b^2
a=√(c^2-b^2)
a=√(5^2-3^2)
a=√(25-9)
a=√(16)
a=4
so cosθ=4/5 answer//
......./|
....../.|
..5./..|
.../....|.3
../___|
.....4
we use the pethagorean theorem to solve for adjacent
c^2=a^2+b^2
a^2=c^2-b^2
a=√(c^2-b^2)
a=√(5^2-3^2)
a=√(25-9)
a=√(16)
a=4
so cosθ=4/5 answer//
2009-05-07 3:57 pm
Draw the triangle. Sin = opposite over hypotenuse, so across from the angle you're working with is a side of 3, and the hypotenuse is 5
Now use Pythagoras: hypotenuse squared = side 1 squared + side 2 squared
5 squared = 3 squared + x squared
x squared = 25 - 9 = 16
x = root 16 = 4
So cos of the angle = adjacent side over hypotenuse
=4/5
Now use Pythagoras: hypotenuse squared = side 1 squared + side 2 squared
5 squared = 3 squared + x squared
x squared = 25 - 9 = 16
x = root 16 = 4
So cos of the angle = adjacent side over hypotenuse
=4/5
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