Answer:
sin theta=0.75 degree, tan theta=1.12 degrees
Step-by-step explanation:
cos theta=2/3
cos theta=cah= Adjacent/hypotenus
so, adjacent=2, hypotenus=3, opposite=?
using Pythagoras theorem
hypotenus(squared)=opposite(squared)+adjacent(squared)
3(squared)=opp(squared)+2(squared)
9=opp(squared)+4
collect like terms
9-4=opp(squared)
opp(squared)=5
root both sides
opp=root of 5
opp=2.24
to find sin theta
sin theta=soh=opposite/hypotenuse
sin theta=2.24/3
sin theta=0.75 degrees
to find tan theta
tan theta=toa= opposite/adjacent
tan theta=2.24/2
tan theta=1.12 degrees
The values of sin θ and tan θ from the given value of cos θ are; sin θ = (√5)/3 and tan θ = (√5)/2
We are told that;
cos θ = 2/3
Now, from trigonometric ratios, we know that;
cos θ = adj/hyp
sin θ = opp/hyp
tan θ = sin θ/cos θ
From right angled triangle;
opp = √(3² - 2²)
opp = √5
Thus;
sin θ = (√5)/3
tan θ = ((√5)/3)/(2/3)
tan θ = (√5)/2
Read more about Trigonometric Ratios at; https://brainly.com/question/11967894
