Ask Question
19 April, 03:39

Find the exact values of the sine, cosine, and tangent of the angle. 255=300-45

+3
Answers (1)
  1. 19 April, 05:47
    0
    Sin 255 = sin (300 - 45) = sin 300 cos 45 - cos 300 sin 45; where sin 300 = - sin (360 - 60) = - sin 60 = - √3/2, sin 45 = cos 45 = 1/√2, cos 300 = cos (360 - 60) = cos 60 = 1/2

    Therefore, sin 255 = (-√3/2) (1/√2) - (1/2) (1/√2) = - √3/2√2 - 1/2√2 = - (√3 + 1) / 2√2 = - (√6 + √2) / 4

    cos 255 = cos (300 - 45) = cos 300 cos 45 + sin 300 sin 45 = (1/2) (1/√2) + (-√3/2) (1/√2) = (1 - √3) / 2√2 = (√2 - √6) / 4

    tan 255 = tan (300 - 45) = (tan 300 - tan 45) / (1 + tan 300 tan 45); where tan 300 = sin 300 / cos 300 = (-√3/2) / (1/2) = - √3 and tan 45 = 1

    Therefore, tan 255 = (-√3 - 1) / (1 + (-√3)) = (-√3 - 1) / (1 - √3) = √3 + 2
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Find the exact values of the sine, cosine, and tangent of the angle. 255=300-45 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers