Learning Objectives

Problem 1 of 3

Prove the identity:

Solution

Problem 2 of 3

If sin θ = (4/5) and sec θ < 0 find the exact value of:

(a) tan 2θ

(b) sin 2θ

Solution

Problem 3 of 3

Find the exact value of:

(a) cos (11π/12)

(b) sec (11π/12)

Solution

cos (11π/12) = (2π/12 + 9π/12) *in order to solve this, you need to find the sums of 11&pi/12, which is π/6 and 3π/4

cos (11π/12) = (π/6 + 3π/4)

cos (11π/12) = cosαcosβ - sinαsinβ

cos (11π/12) = cos(π/6)cos(3π/4) - sin(π/6)sin(3π/4)

cos (11π/12) = (√3/2)(-√2/2) - (1/2)(√2/2)

cos (11π/12) = -√6/4 - √2/4

cos (11π/12) = (-√6 - √2)/4

since sec is the reciprocal of cosine. the answer is:

4/(-√6 - √2)