Answer:
cos2∅= -0.557
tan2∅= --1.49
Step-by-step explanation:
Given:
cos∅=-8/17
By trigonometric ratios:
as cos∅=adjacent/hypotenuse
hypotenuse= 17
adjacent=-8
Now finding perpendicular using Pythagoras theorem:
c2=a2+b2
17^2=(-8)^2+b^2
289-64=b^2
b^2=225
b=±15
b=-15 as ∅ is in third quadrant so both the opposite and adjacent sides be in 3rd quadrant
tan∅=opposite/adjacent
tan∅=-15/-8
sin∅=-15/17
Now finding cos2∅
cos2∅= 1-2sin^2∅
=1 - 2(-15/17)^2
=1 -450/289
= -161/289
=-0.557
finding tan2∅
tan2∅= 2tan∅/1-tan^2∅
= 2(-15/-8) / 1-(-15/-8)^2
= (15/4) / 1-225/64
=(15/4) / (-161/64)
= -240/161
=-1.49 !
