Find three equivalent trig ratios to sin 110 degrees.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

sin(110), this can be rewritten as sin(180-70).

Now we know from basic trignometry,

`sin(180-theta) = sin(theta)`

Therefore,

sin(110) = sin(70)

sin(70) can be rewritten as sin(90-20). According to basic trignometry,

`sin(90-theta) =cos(theta)`

Therefore, sin(70) = cos(20), so sin(110) = cos(20)

`cos(360-theta) =cos(theta)`

cos(20) = cos(360-20)

cos(20) = cos(340)

Therefore sin(110)...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

sin(110), this can be rewritten as sin(180-70).

Now we know from basic trignometry,

`sin(180-theta) = sin(theta)`

Therefore,

sin(110) = sin(70)

sin(70) can be rewritten as sin(90-20). According to basic trignometry,

`sin(90-theta) =cos(theta)`

Therefore, sin(70) = cos(20), so sin(110) = cos(20)

`cos(360-theta) =cos(theta)`

cos(20) = cos(360-20)

cos(20) = cos(340)


Therefore sin(110) = cos(340)

 

Three equivalent trig ratios are,

sin(110) = sin(70) =cos(20) = cos(340)

Approved by eNotes Editorial Team