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Find the six trigonometric functions of 0 in simplest radical form. Rationalize all fractions.

Find the six trigonometric functions of 0 in simplest radical form. Rationalize all-example-1
User ElToro
by
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1 Answer

2 votes

step 1

Find the hypotenuse of the right triangle

applying Pythagorean theorem

c^2=2^2+3^2

c^2=4+9


c=\sqrt[]{13}

step 2

Find sin(theta)

we have


\sin (\theta)=\frac{2}{\sqrt[]{13}}

simplify


\sin (\theta)=\frac{2}{\sqrt[]{13}}=\frac{2\sqrt[\square]{13}}{13}

opposite side divided by the hypotenuse

step 3

Find cos(theta)


\cos (\theta)=\frac{3}{\sqrt[\square]{13}}

adjacent side divided by the hypotenuse

simplify


\cos (\theta)=\frac{3}{\sqrt[\square]{13}}=\frac{3\sqrt[]{13}}{13}

step 4

find tan(theta)


\tan (\theta)=(2)/(3)

opposite side divided by the adjacent side

step 5

find cot(theta)


\cot (\theta)=(1)/(\tan (\theta))=(3)/(2)

adjacent side divided by the opposite side

step 6

Find sec(theta)


\sec (\theta)=(1)/(\cos (\theta))=\frac{\sqrt[]{13}}{3}

hypotenuse divided by the adjacent side

step 7

Find csc(theta)


\csc (\theta)=(1)/(\sin (\theta))=\frac{\sqrt[]{13}}{2}

hypotenuse divided by the opposite side

User Nthalk
by
8.3k points
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