Question

1. Draw a right triangle with sides 2,2√3, and 4 units. Label all angle measures and sides. Using the side relationships from the figure, show that the following trigonometric identities hold true for either one of the non-right angles:

a. tan 0=sin 0/cos O
b.) sin^2(0)+cos^2(0)=1
where 0 represents whichever angle you choose

FYI...all of the 0 have a line through them
THank you because I don't understand this at all.

Answer 1

see the picture attached to better understand the problem

we know that
in a right triangle ABC
sin ∅=opposite side angle ∅/hypotenuse
cos ∅=adjacent side angle ∅/hypotenuse
tan ∅=opposite side angle ∅/adjacent side angle ∅

in this problem
opposite side angle ∅=2 units
adjacent side angle ∅=2√3 units
hypotenuse=4 units
so
sin ∅=2/4----> 1/2
cos ∅=2√3/4----> √3/2
tan ∅=2/2√3----> 1/√3----> √3/3

Part a) show that the following trigonometric identities hold true for either one of the non-right angles:
tan ∅=sin ∅/cos ∅
sin ∅=1/2
cos ∅=√3/2
tan ∅=(1/2)/(√3/2)--> (1/2)*2/√3---> 1/√3--->1/√3*(√3/√3)---> √3/3--> is ok

Part b) show that the following trigonometric identities hold true for either one of the non-right angles:
sin² ∅+cos² ∅=1
sin ∅=1/2
cos ∅=√3/2
so
(1/2)²+(√3/2)²=1------> 1/4+3/4----> 4/4----> 1=1----> is ok