Find the six function values of 8∘ in terms of p, q and r, if sin⁡82∘=p cos⁡82∘=q tan⁡82∘=r

Recall that, cs⊗=sin⁡(90∘−x), sin⁡x=cos⁡(90∘−x), cot⁡x=tan⁡(90∘−x), tan⁡x=cot⁡(90∘−x), Therefore, sin⁡8∘=cos⁡82∘ sin⁡8∘=q cos⁡8∘=sin⁡82∘ cos⁡8∘=p cot⁡8∘=tan⁡82∘ cor8∘=r csc⁡8∘=1sin⁡8∘ csc⁡8∘=1q sec⁡8∘=1cos⁡8∘ sec⁡8∘=1p tan⁡8∘=1cot⁡8∘ tan⁡8∘=1r

Answered: "Find the six function values of 8∘ in..."

Trent Carpenter

Answered question

2020-11-08

Find the six function values of

8^{\circ}

in terms of p, q and r, if

{\sin 82}^{\circ} = p

{\cos 82}^{\circ} = q

{\tan 82}^{\circ} = r

Answer & Explanation

grbavit

Skilled2020-11-09Added 109 answers

Recall that,

c s \otimes = \sin (90^{\circ} - x),

\sin x = \cos (90^{\circ} - x),

\cot x = \tan (90^{\circ} - x),

\tan x = \cot (90^{\circ} - x),

Therefore,

{\sin 8}^{\circ} = {\cos 82}^{\circ}

{\sin 8}^{\circ} = q

{\cos 8}^{\circ} = {\sin 82}^{\circ}

{\cos 8}^{\circ} = p

{\cot 8}^{\circ} = {\tan 82}^{\circ}

c or 8^{\circ} = r

{\csc 8}^{\circ} = \frac{1}{{\sin 8}^{\circ}}

{\csc 8}^{\circ} = \frac{1}{q}

{\sec 8}^{\circ} = \frac{1}{{\cos 8}^{\circ}}

{\sec 8}^{\circ} = \frac{1}{p}

{\tan 8}^{\circ} = \frac{1}{{\cot 8}^{\circ}}

{\tan 8}^{\circ} = \frac{1}{r}

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