For what angle is sin θ + cos θ = 2.34?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

i don't get it but i hope this helps

  θ ≈ 0.785398 -1.089533i radians

Step-by-step explanation:

The sum of the sine and cosine can never exceed √2 for real-valued angles. The angle that gives this sum is the complex angle ...

  θ ≈ 0.785398 -1.089533i radians

Additional comment

  sin(θ) +cos(θ) = √2·cos(θ-π/4)

We want the value of this to be 2.34, so ...

  2.34 = √2·cos(θ -π/4)

  cos(θ -π/4) = 2.34/√2

  θ -π/4 = arccos(1.17√2)

  θ = π/4 +arccos(1.17√2)

A suitable calculator can provide the complex value of the arccos of a number greater than 1.

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