Question

find an angle \\( \theta \\) with \\( 0^{\circ}<\theta<360^{\circ} \\) that has the same:
sine as \\( 50^{\circ}: \theta= \\) degrees
cosine as \\( 50^{\circ}: \theta= \\) degrees
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Explanation:

Step1: Find the angle with the same sine as \(50^{\circ}\)

We know that \(\sin\theta=\sin(180^{\circ}-\theta)\).
If \(\theta_1 = 50^{\circ}\), then \(\theta_2=180^{\circ}- 50^{\circ}=130^{\circ}\)

Step2: Find the angle with the same cosine as \(50^{\circ}\)

We know that \(\cos\theta=\cos(360^{\circ}-\theta)\).
If \(\theta_1 = 50^{\circ}\), then \(\theta_2 = 360^{\circ}-50^{\circ}=310^{\circ}\)

Answer:

Sine as \(50^{\circ}\): \(\theta = 130\) degrees
Cosine as \(50^{\circ}\): \(\theta = 310\) degrees