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Answer :
Final answer:
The two angles which satisfy the equation cos (5x - 121) = sin (x + 54) are 16.5° and 376.5°. However, since trigonometric functions are periodic, the second solution 376.5° is also equivalent to 16.5°.
Explanation:
This question revolves around the concept of co-function identities in trigonometry. To find the two angles, we need to understand the relationship between cosine and sine functions. According to the co-function identity, cos(90 - α) = sin(α), which means cos (5x - 121) = sin (x + 54) translates to 5x - 121 = 90 - (x + 54).
Solving this equation gives the first solution as x = 16.5°, which is the first angle. For the second angle, sine and cosine functions are periodic with a period of 360°, so adding 360° to the first angle gives the second solution, x = 16.5 + 360 = 376.5°. After converting to the range from 0° to 360°, the second angle is 16.5°.
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