Find the Other Trig Values in Quadrant I tan(A)=0.7353

$\tan (A) = 0.7353$

Use the definition of tangent to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

$\tan (A) = \frac{opposite}{adjacent}$

Find the hypotenuse of the unit circle triangle. Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

$Hypotenuse = \sqrt{{opposite}^{2} + {adjacent}^{2}}$

Replace the known values in the equation.

$Hypotenuse = \sqrt{{(0.7353)}^{2} + {(1)}^{2}}$

Simplify inside the radical.

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Raise $0.7353$ to the power of $2$ .

Hypotenuse $= \sqrt{0.54066609 + {(1)}^{2}}$

One to any power is one.

Hypotenuse $= \sqrt{0.54066609 + 1}$

Add $0.54066609$ and $1$ .

Hypotenuse $= \sqrt{1.54066609}$

Find the value of sine.

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Use the definition of sine to find the value of $\sin (A)$ .

$\sin (A) = \frac{opp}{hyp}$

Substitute in the known values.

$\sin (A) = \frac{0.7353}{\sqrt{1.54066609}}$

Simplify the value of $\sin (A)$ .

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Multiply $\frac{0.7353}{\sqrt{1.54066609}}$ by $\frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$ .

$\sin (A) = \frac{0.7353}{\sqrt{1.54066609}} \cdot \frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$

Combine and simplify the denominator.

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Multiply $\frac{0.7353}{\sqrt{1.54066609}}$ and $\frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Raise $\sqrt{1.54066609}$ to the power of $1$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Raise $\sqrt{1.54066609}$ to the power of $1$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{\sqrt{1.54066609}}^{1 + 1}}$

Add $1$ and $1$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{\sqrt{1.54066609}}^{2}}$

Rewrite ${\sqrt{1.54066609}}^{2}$ as $1.54066609$ .

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Rewrite $\sqrt{1.54066609}$ as ${1.54066609}^{\frac{1}{2}}$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{({1.54066609}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{1.54066609}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{1.54066609}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{{1.54066609}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{1.54066609}$

Evaluate the exponent.

$\sin (A) = \frac{0.7353 \sqrt{1.54066609}}{1.54066609}$

Multiply $0.7353$ by $\sqrt{1.54066609}$ .

$\sin (A) = \frac{0.91268061}{1.54066609}$

Divide $0.91268061$ by $1.54066609$ .

$\sin (A) = 0.59239352$

Find the value of cosine.

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Use the definition of cosine to find the value of $\cos (A)$ .

$\cos (A) = \frac{adj}{hyp}$

Substitute in the known values.

$\cos (A) = \frac{1}{\sqrt{1.54066609}}$

Simplify the value of $\cos (A)$ .

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Multiply $\frac{1}{\sqrt{1.54066609}}$ by $\frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$ .

$\cos (A) = \frac{1}{\sqrt{1.54066609}} \cdot \frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$

Combine and simplify the denominator.

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Multiply $\frac{1}{\sqrt{1.54066609}}$ and $\frac{\sqrt{1.54066609}}{\sqrt{1.54066609}}$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Raise $\sqrt{1.54066609}$ to the power of $1$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Raise $\sqrt{1.54066609}$ to the power of $1$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{\sqrt{1.54066609} \sqrt{1.54066609}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\cos (A) = \frac{\sqrt{1.54066609}}{{\sqrt{1.54066609}}^{1 + 1}}$

Add $1$ and $1$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{{\sqrt{1.54066609}}^{2}}$

Rewrite ${\sqrt{1.54066609}}^{2}$ as $1.54066609$ .

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Rewrite $\sqrt{1.54066609}$ as ${1.54066609}^{\frac{1}{2}}$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{{({1.54066609}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{{1.54066609}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{{1.54066609}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\cos (A) = \frac{\sqrt{1.54066609}}{{1.54066609}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\cos (A) = \frac{\sqrt{1.54066609}}{1.54066609}$

Evaluate the exponent.

$\cos (A) = \frac{\sqrt{1.54066609}}{1.54066609}$

Evaluate the root.

$\cos (A) = \frac{1.24123571}{1.54066609}$

Divide $1.24123571$ by $1.54066609$ .

$\cos (A) = 0.80564875$

Find the value of cotangent.

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Use the definition of cotangent to find the value of $\cot (A)$ .

$\cot (A) = \frac{adj}{opp}$

Substitute in the known values.

$\cot (A) = \frac{1}{0.7353}$

Divide $1$ by $0.7353$ .

$\cot (A) = 1.35998912$

Find the value of secant.

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Use the definition of secant to find the value of $\sec (A)$ .

$\sec (A) = \frac{hyp}{adj}$

Substitute in the known values.

$\sec (A) = \frac{\sqrt{1.54066609}}{1}$

Divide $\sqrt{1.54066609}$ by $1$ .

$\sec (A) = \sqrt{1.54066609}$

Find the value of cosecant.

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Use the definition of cosecant to find the value of $\csc (A)$ .

$\csc (A) = \frac{hyp}{opp}$

Substitute in the known values.

$\csc (A) = \frac{\sqrt{1.54066609}}{0.7353}$

Simplify the value of $\csc (A)$ .

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Evaluate the root.

$\csc (A) = \frac{1.24123571}{0.7353}$

Divide $1.24123571$ by $0.7353$ .

$\csc (A) = 1.68806706$

This is the solution to each trig value.

$\sin (A) = 0.59239352$

$\cos (A) = 0.80564875$

$\tan (A) = 0.7353$

$\cot (A) = 1.35998912$

$\sec (A) = \sqrt{1.54066609}$

$\csc (A) = 1.68806706$

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