If sin(α) =21/29 where 0 < α <π/2 and cos(β) =7/25 where 3π/2 < β < 2π, find the exact values of the following.

Question

If sin(α) =21/29 where 0 < α <π/2  and cos(β) =7/25 where 3π/2 < β < 2π, find the exact values of the following.

(a)    sin(α + β)

 

(b)    cos(α − β)

 

(c)    tan(α − β)

 

Answer 1

Use Pythagoras to determine cos α and sin β

sin α = 21/29

cos α = 20/29.

cos β = 7/25

sin β = -24/25

Now look up the sum/difference formulas in your text and apply the appropriate one to each

Answer 2

sin(α) =21/29

α=46.397...........

cos(β) =7/25

cosβ=.28

β=73.739...........

β is between 270° and 360°; so β=????????

The best I can do is 253°.