if sinØ=cosØ then find the value of Ø
To find the value of Ø when sinØ = cosØ, we can use the basic trigonometric identity that states: sin²Ø + cos²Ø = 1.
Since sinØ = cosØ, we can substitute cosØ for sinØ in the identity:
cos²Ø + cos²Ø = 1
Combining like terms:
2cos²Ø = 1
Divide both sides by 2:
cos²Ø = 1/2
Now, since cosine is positive in the first and fourth quadrants, we can take the square root of both sides:
cosØ = ±√(1/2)
This means that Ø can be any angle where the cosine value is ±√(1/2). These angles occur at θ = π/4, 7π/4, 5π/4, and 3π/4.
So, the possible values of Ø are Ø = π/4, 7π/4, 5π/4, and 3π/4.
divide both sides by cosØ
tan Ø = 1
Ø = 45° or Ø = 225° (in quad III)
Ø = π/4 or Ø = 5π/4 for 0 ≤ Ø ≤ 2π