52. The point on the unit circle that corresponds to ⎝ ⎠ 1 3 ⎞ θ = 5π = 150º is ⎛ − 240º = 4π ⎜ − − ⎟ is , . θ = ⎛ 3 , 1 ⎞ . ⎜ ⎟ 3 ⎝ ⎠ 2 2 sin 240º =− 6 2 ⎝ 2 2 ⎠ = sin 5π 1 cos 240º = − 1 6 2 2 cos 5π =− 3 3 6 2 ⎛ 1 ⎞ ⎛ ⎞ 3 ⎜= − ⎟ ⎛ ⎞ ⎜ ⎟ 2 ⎟ = 3 2 ⎠ = − 3 ⋅ ⎜ − tan 240º = ⎝ tan 5π = − 3 = 1 2 ⎞ ⋅ 3 = ⎝ 2 ⎠ ⋅ ⎛ − 6 ⎛ 3 ⎞ 2 ⎜ 3 ⎟ 3 3 ⎛ − 1 ⎞ 2 ⎝ 1 ⎠ ⎜ − ⎟ ⎝ ⎠ ⎜ ⎟ 2 ⎝ 2 ⎠ ⎝ ⎠ csc 240º = 1 = 1⋅ ⎛ − 2 ⎞ ⋅ 3 = − 2 3 csc 5π = ⎛ ⎞ ⎜ ⎟ 3 1 = 1⋅ 2 = 2 ⎛ ⎞ 6 1 1 ⎜ − ⎟ ⎝ ⎠ 3 3 3 ⎜ ⎟ ⎝ ⎠ = sec 5π = ⎛ 2 ⎞ ⋅ 1⋅ 3 = − 2 3 1 sec 240º = 1 = 1⋅ ⎛ − 2 ⎞ = − 2 − 6 ⎛ 3 ⎞ ⎜ ⎟ ⎛ − ⎞ ⎝ ⎠ 3 3 3 1 1 ⎜ − ⎟ ⎝ ⎠ ⎜ 2 ⎟ ⎝ 2 ⎠ ⎝ ⎠ ⎛ − 1 ⎞ ⎛ 3 ⎞ 1 ⎛ 2 ⎞ ⎜ 2 ⎟ 3 3 − π ⎜ ⎟ = − ⋅ ⎜ − cot 240º = ⎝ ⎠ ⎟ ⋅ = cot 5 2 1 ⎛ 1 ⎞ ⎠ 3 3 3 ⋅ 2 6 = − ⎛ 3 ⎞ 2 ⎝ 3 = ⎝ 2 ⎠ = − 3 ⎜ − ⎟ ⎜ ⎟ ⎝ ⎠ 2 ⎝ ⎠
⎝ ⎠ 52. The point on the unit circle that corresponds to θ = 5π = 150º is ⎛ − 3 , 1 ⎞ . θ = 240º = 4π ⎛ 1 3 ⎞ is ⎜ − , − ⎟ . ⎜ ⎟ 3 ⎝ 2 2 ⎠ 6 sin 5π = 1 6 2 cos 5π =− 3 ⎝ 2 2 ⎠ 3 sin 240º =− 2 cos 240º = − 1 2 6 2 ⎛ 1 ⎞ ⎛ 3 ⎞ ⎜= − ⎟ ⎛ ⎞ ⎜ ⎟ tan 240º = ⎝ 2 ⎠ = − 3 ⋅ ⎜ − 2 ⎟ = 3 tan 5π = ⎝ 2 ⎠ = 1 ⋅ ⎛ − 2 ⎞ ⋅ 3 = − 3 6 ⎛ 3 ⎞ 2 ⎜ 3 ⎟ 3 3 ⎛ − 1 ⎞ 2 ⎝ 1 ⎠ ⎜ − ⎟ ⎝ ⎠ ⎜ 2 ⎟ ⎝ 2 ⎠ ⎝ ⎠ csc 240º = 1 = 1⋅ ⎛ − 2 ⎞ ⋅ 3 = − 2 3 csc 5π = 1 = 1⋅ 2 = 2 ⎛ ⎞ ⎜ ⎟ 3 6 ⎛ 1 ⎞ 1 ⎜ − 3 ⎟ ⎝ 3 ⎠ 3 ⎜ ⎟ ⎝ ⎠ sec 5π = 1 = 1⋅ ⎛ − 2 ⎞ ⋅ 3 = − 2 3 sec 240º = 1 = 1⋅ ⎛ − 2 ⎞ = − 2 6 ⎛ 3 ⎞ ⎜ 3 ⎟ 3 3 ⎛ − 1 ⎞ ⎝ 1 ⎠ ⎜ − ⎟ ⎝ ⎠ ⎜ 2 ⎟ ⎝ 2 ⎠ ⎝ ⎠ ⎛ − 1 ⎞ ⎛ 3 ⎞ − ⎜ 2 ⎟ 1 ⎛ 2 ⎞ 3 3 π ⎜ ⎟ cot 240º = ⎝ ⎠ = − ⋅ ⎜ − ⎟ ⋅ = cot 5 6 = ⎝ 2 ⎛ 1 ⎞ ⎠ = − 3 ⋅ 2 = − 3 2 1 ⎛ 3 ⎞ ⎜ − ⎟ 2 ⎝ 3 ⎠ 3 3 ⎜ ⎟ ⎝ 2 ⎠ ⎝ ⎠
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