Help with Trig hw PLEASE?

a) sec(theta) > 0 means cos(theta) > 0, as sec and cos are reciprocals. sin(theta) > 0 also, so you have both sine and cosine positive -- theta is in quadrant 1.

b) cot(theta) < 0 means that sin(theta) or cos(theta) < 0, but not both (minus/minus = plus). You got cos(theta) > 0, so sin(theta) < 0. Positive cosine and negative sine mean that theta is in quadrant 4.

First remember the primary trigonometry functions:

sin θ

cos θ

tan θ

Now remember the reciprocal functions:

csc θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

The primary and reciprocal functions will have the same sign.

PROBLEM 1:

sin θ > 0 (positive)

sec θ = 1/cos θ > 0 (positive)

sin θ is positive in quadrant 1 and 2.

cos θ is positive in quadrant 1 and 4

Thus the place where they are both positive is quadrant 1.

Answer:

Quadrant 1

PROBLEM 2:

cot θ = 1/tan θ < 0 (negative)

cos θ > 0 (positive)

tan θ is positive in quadrant 1 and 3, so it is negative in quadrants 2 and 4.

cos is positive in quadrants 1 and 4

Thus the place where tangent (or cot) is negative and cos is positive is 4.

Answer:

Quadrant 4

Remember the mnemonic "All Students Take Calculus"

Quadrant 1 - All = All functions are positive

Quadrant 2 - Students = Sine (or 1/sin = csc) function is positive

Quadrant 3 - Take = Tangent (or 1/tan = cot) function is positive

Quadrant 4 - Calculus = Cosine (or 1/cos = sec) function is positive

See the diagram below:

rule

Quadrant 1 --> all positive (sin >0 , cos >0 , tan >0)

Quadrant 2 --> only sin>0

Quadrant 3 --> only tan>0

Quadrant 4 --> only cos>0

a) Quadrant 1

b) Quadrant 4

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