Answer:
a) -tan(π/4) = -1
b) -1/sin(π/3) = -(2/3)√3
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