# Find the values of the trigonometric functions of θ if tan θ = 3/4 and is in the 3rd quadrant.

2
by yhen2

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by yhen2

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Sin = -3/5

cos = -4/5

tan = 3/4

csc = -5/3

sec = -5/4

cot = 4/3

cos = -4/5

tan = 3/4

csc = -5/3

sec = -5/4

cot = 4/3

If

y = 3

x = 4

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If we are to draw a triangle in representation for the angle, x and y are the legs of the triangle. For us to find the hypotenuse, let us use Pythagorean Theorem.

c² = x² + y²

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c² = x² + y²

c² = 4² + 3²

c² = 25

c = √25

c = 5

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sine α = opposite/hypotenuse

or in this case,

sine α = y/c

Since y in the 3rd quadrant is negative, then take the negative of y

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cosine α = adjacent/hypotenuse

or in this case,

cos α = x/c

Since x in the 3rd quadrant is negative, then take the negative of x

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cotangent α = cosine/sine

cot α = (4/5)/(3/5)

5 will be cancelled out

Both x and y in the 3rd quadrant are negative and negative over negative is positive, then it will have a positive sign

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secant α = 1/cosine α

sec α = 1/(4/5)

Since x in the 3rd quadrant is negative, then take the negative of x

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cosecant = 1/sine α

csc α = 1/(3/5)

Since y in the 3rd quadrant is negative, then take the negative of y

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see attachment