Given that sinA=2/5 and that A is obtuse,find the value of cosA.
sinA = 2/5, so
cosA = √21/5
But A is in QII, so cosA = -√21/5
Why not sqrt(5^2-2^2)/5 ?
To find the value of cosA, we can use the Pythagorean Identity of trigonometric functions which states that sin²A + cos²A = 1.
Given that sinA = 2/5, we can square it:
(sinA)² = (2/5)²
= 4/25
Now, we can substitute this value into the Pythagorean Identity:
(4/25) + cos²A = 1
Next, let's solve for cos²A by subtracting 4/25 from both sides:
cos²A = 1 - 4/25
= 25/25 - 4/25
= 21/25
Since A is an obtuse angle, cosA will be negative. Therefore, we can find the value of cosA by taking the square root of 21/25, and multiplying it by -1:
cosA = -√(21/25)
= -(√21 / √25)
= -√21 / 5
Therefore, the value of cosA is -√21 / 5.