For each of the indicated intervals describe whether the cos

For each of the indicated intervals, describe whether the cosine and sine of are positive or negative and determine whether they are increasing or decreasing.

(a) 0 < < 2

(b) 2 < <

(c) < < 3 2

(d) 3 2 < < 2

Cosine: positive and increasing, positive and decreasing, negative and increasing, negative and decreasing

Sine: positive and increasing positive and decreasing negative and increasing negative and decreasing

Solution

(a) 0 < < /2 =========> Sine positive and increasing, Cosine positive and decreasing

(b) /2 < < =======> Sine positive and decreasing, Cosine negative and increasing

(c) < < 3/2 ======> Sine negative and increasing, Cosine negative and decreasing

(d) 3/2 < < 2 ========> Sine negative and decreasing, Cosine positive and increasing