sec( theta+45)=1

Question

We are doing simple trig equations, you know, where like 1/2 =cos(theta) and you find on the trig circle what that is equal to. So it would be 60 and 300 degrees. However, I don't know how to solve this problem:

 

sec( theta+45)=1

 

Please help! Thanks!

Answer 1

sec(θ+45°) = 1/cos(θ+45°)

 

1/cos(θ+45°) = 1

1 = cos(θ+45°)

 

The cosine equals one at 0^o ± k·360°, k = 0, 1, 2, 3, ...  Solve for θ.