# Find the values of the trigonometric functions of t from the given information?

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1.) sec t = 3, terminal point of t is in quadrant 4

2.) sin t = -1/4, sec t < 0

Please show the steps… thanks!

• 1)

sec t = 3 ==>hypotenuse / adj. side = 3/1

hypotenuse = 3, adj. side = 1

opposite side = √(9 – 1) = 2√2

in IV quadrant only cos and sec are positive

sin t= – 2√2 / 3 , csc t = – 3 / (2√2)

cos t = 1/3

tan t = -2√2, cot t = -1 /(2 √2)

2)

sin t = -1/4===> opposite side = 1, hypotenuse = 4

adj. side = √(4^2 – 1) = √15

since sec and sin are negative, t is in III quadrant, where only tan and cot are positive.

sin t = -1/4, csc t = -4

cos t = -√15 / 4, sec t = -4 /√15

tan t = 1/√15, cot t = √15

• cost=-4/5=> t=arc cos(-4/5)=> t=143* 8′ or 216*fifty two’eleven” simply by fact cost is -ve interior the II & III quadrants. Now attitude t is had to terminate interior the III quadrant, so the respond is t=216* fifty two’ eleven”.

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