Question

Please explain your answer. THX!

Answer 1

Answer:

see explanation

Step-by-step explanation:

(3)

Given cosΘ = - $\frac{4}{5}$

Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )

Since Θ in second quadrant then sinΘ > 0

sinΘ = $\frac{3}{5}$

Using the trigonometric identity

sin2Θ = 2sinΘcosΘ, then

sin2Θ = 2 × $\frac{3}{5}$ × - $\frac{4}{5}$ = - $\frac{24}{25}$

(4)

Using the trigonometric identity

cos(x - y) = cosxcosy + sinxsiny

note cos15° = cos(45 - 30)°

cos(45 - 30) = cos45cos30 + sin45sin30

                    = ( $\frac{\sqrt{2} }{2}$ × $\frac{\sqrt{3} }{2}$) + ($\frac{\sqrt{2} }{2}$ × $\frac{1}{2}$)

                    = $\frac{\sqrt{2(\sqrt{3}+1) } }{4}$