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asambeis [7]
3 years ago
14

If the angles are represented in degrees, find both angles: sin(x+7)=cos(4x+8)

Mathematics
1 answer:
garri49 [273]3 years ago
7 0

Answer:

m\angle 1 = 22\degree

m\angle 2 = 68\degree

Step-by-step explanation:

\sin(x + 7) =  \cos(4x + 8) \\  \sin(x + 7) =  \sin \{90  - (4x + 8) \} \\  \{ \because \cos \theta =  \sin(90 \degree -  \theta)  \}\\  \therefore \: (x + 7) = 90 - (4x + 8) \\ x + 7 + 4x + 8 = 90 \\ 5x = 90 - 15 \\ 5x = 75 \\ x =  \frac{75}{5}  \\ x = 15

(x + 7)° = (15 + 7)° = 22°

(4x + 8)° = (4*15 + 8)° = (60 + 8)° = 68°

m\angle 1 = 22\degree

m\angle 2 = 68\degree

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