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प्रश्न
Find the value of:
sec (–855°)
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उत्तर
We simplify the angle by adding or subtracting multiples of 360° until we get an angle between 0° and 360°.
−855∘ + 3 × 360∘ = −855∘ + 1080∘ = 225∘
sec (−855∘) = sec (225∘)
225∘ is in the third quadrant, where cosine is negative.
Reference angle: 225∘ − 180∘ = 45∘
cos (225∘) = −cos (45∘) = `-1/sqrt2`
sec (225∘) = `1/cos(225^\circ) = 1/(-1/sqrt2) = -sqrt2`
sec (−855∘) = `-sqrt2`
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