Question

Please someone help with that

Answer 1

Answer:

  a) -tan(π/4) = -1

  b) -1/sin(π/3) = -(2/3)√3

Step-by-step explanation:

The given functions are reciprocals of the primary trig functions:

  cot(x) = 1/tan(x)

  csc(x) = 1/sin(x)

The tangent function has a period of π, and is equal to the cotangent of the complementary angle.

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a)

The given angle is an alias of -π/4, so we can write ...

  cot(7π/4) = cot(-π/4) = -cot(π/4) = -tan(π/2 -π/4) = -tan(π/4)

  -tan(π/4) = -1

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b)

  csc(-π/3) = 1/sin(-π/3) = -1/sin(π/3) = -1/(√3/2) = -2/√3

  -1/sin(π/3) = -2√3/3