To find the value of angle A given the equation 2sin²A - 1/3 = cos²A, we can use trigonometric identities to simplify the equation.
We know that sin²A + cos²A = 1 (Pythagorean identity) and cos²A = 1 - sin²A.
Substitute the value of cos²A in the equation:
2sin²A - 1/3 = 1 - sin²A
Now, simplify the equation:
3sin²A - 1 = 3 - 3sin²A
6sin²A = 4
sin²A = 4/6
sin²A = 2/3
Take the square root of both sides to find sinA:
sinA = √(2/3)
Now, find the value of angle A by taking the inverse sine function (sin⁻¹) of √(2/3):
A = sin⁻¹(√(2/3))
Therefore, the value of angle A in radians is sin⁻¹(√(2/3)).
GIVEN THAT A IS ACUTE AND 2 SIN² A - 1/3 = COS ² A .FIND ANGEL A
3 answers
somehow you went off the rails. Let's start with
2sin²A - 1/3 = 1 - sin²A
3sin²A = 4/3
sin²A = 4/9
sinA = ±2/3
if sinA = 2/3 then A ≈ 41.8° or 138.2°
if sinA = -2/3 then A ≈ 221.8° or 318.2°
2sin²A - 1/3 = 1 - sin²A
3sin²A = 4/3
sin²A = 4/9
sinA = ±2/3
if sinA = 2/3 then A ≈ 41.8° or 138.2°
if sinA = -2/3 then A ≈ 221.8° or 318.2°
Apologies for the mistake in my previous response. Thank you for correcting it.
Given the equation 2sin²A - 1/3 = 1 - sin²A, following your steps, we arrive at:
3sin²A = 4/3
sin²A = 4/9
sinA = ±2/3
If sinA = 2/3, then Angle A can be approximately 41.8° or 138.2°.
If sinA = -2/3, then Angle A can be approximately 221.8° or 318.2°.
Thank you for pointing out the error.
Given the equation 2sin²A - 1/3 = 1 - sin²A, following your steps, we arrive at:
3sin²A = 4/3
sin²A = 4/9
sinA = ±2/3
If sinA = 2/3, then Angle A can be approximately 41.8° or 138.2°.
If sinA = -2/3, then Angle A can be approximately 221.8° or 318.2°.
Thank you for pointing out the error.