If sin theta=3/5 THen cos theta wil be
sin Ø = 3/5 , so Ø could be in quadrants I or II
make a sketch of the triangle and you should recognize the 3-4-5 right-angled triangle.
the cosØ = 4/5 if Ø is in I
and cosØ = - 4/5 if Ø is in II
To find the value of cos(theta) when sin(theta) is given, we can use the identity:
sin^2(theta) + cos^2(theta) = 1
Given that sin(theta) = 3/5, we can substitute this value into the equation above:
(3/5)^2 + cos^2(theta) = 1
Expanding and simplifying:
9/25 + cos^2(theta) = 1
Next, we isolate cos^2(theta) by subtracting 9/25 from both sides:
cos^2(theta) = 1 - 9/25
cos^2(theta) = 25/25 - 9/25
cos^2(theta) = 16/25
Finally, taking the square root of both sides, we find:
cos(theta) = ±√(16/25)
Since cosine can be either positive or negative, the two possible values for cos(theta) are:
cos(theta) = ±4/5