Answer to Question #343111 in Trigonometry for Sunshine

Question #343111

If cos(πœƒ ) = 3/5 and tan( πœƒ ) < 0 , find the exact value of each of the remaining trigonometric functions of πœƒ


1
Expert's answer
2022-05-24T17:41:43-0400

"\\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta}<0" and "\\cos\\theta=\\frac 35>0" so we can conclude "\\sin\\theta<0"

From "\\sin^2\\theta+\\cos^2\\theta=1" we can write

"\\sin\\theta=-\\sqrt{1-\\cos^2\\theta}=-\\sqrt{1-9\/25}=-4\/5"

"\\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta}=\\frac35:(-\\frac45)=-\\frac34"

"\\cot\\theta=\\frac{1}{\\tan\\theta}=-\\frac43"

"\\sec\\theta=\\frac{1}{\\cos\\theta}=\\frac53"

"\\csc\\theta=\\frac{1}{\\sin\\theta}=-\\frac54"


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