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secondary 4 | A Maths
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Date Posted: 2 years ago
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If you use addition/compound angle formula, you will get cos 345°.
cos 357° cos 12° + sin 357° sin 12°
= cos (357° - 12°)
= cos 345°
The corresponding basic reference angle of 345° is 15°, and we know that the cosine of a fourth quadrant angle spews out a positive number, so
cos 345° = cos 15°
We express 15° as the difference of two angles, say 45° - 30° before using the addition/compound angle formula again.
cos 15°
= cos (45° - 30°)
= cos 45° cos 30° + sin 45° sin 30°
You will get 1/4 multiplied by (sqrt 6 + sqrt 2) or something like that after simplification. I leave you to proceed on from this step.
cos 357° cos 12° + sin 357° sin 12°
= cos (357° - 12°)
= cos 345°
The corresponding basic reference angle of 345° is 15°, and we know that the cosine of a fourth quadrant angle spews out a positive number, so
cos 345° = cos 15°
We express 15° as the difference of two angles, say 45° - 30° before using the addition/compound angle formula again.
cos 15°
= cos (45° - 30°)
= cos 45° cos 30° + sin 45° sin 30°
You will get 1/4 multiplied by (sqrt 6 + sqrt 2) or something like that after simplification. I leave you to proceed on from this step.
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