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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