Find the Other Trig Values in Quadrant I tan(A) equals zero point seven eight

$\tan (A) = 0.78$

Use the definition of tangent to find the known sides of the unit circle right triangle. Each value's sign is defined by the quadrant.

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

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.

$Hypotenuse = \sqrt{{(0.78)}^{2} + {(1)}^{2}}$

Clarify inside the radical.

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Raise $0.78$ to the power of $2$ .

Hypotenuse $= \sqrt{0.6084 + {(1)}^{2}}$

One raised to any power equals one.

Hypotenuse $= \sqrt{0.6084 + 1}$

Add $0.6084$ and $1$ .

Hypotenuse $= \sqrt{1.6084}$

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.

$\sin (A) = \frac{0.78}{\sqrt{1.6084}}$

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

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First, multiply $\frac{0.78}{\sqrt{1.6084}}$ by $\frac{\sqrt{1.6084}}{\sqrt{1.6084}}$ .

$\sin (A) = \frac{0.78}{\sqrt{1.6084}} \cdot \frac{\sqrt{1.6084}}{\sqrt{1.6084}}$

Add and Clarify the denominator.

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Multiply $\frac{0.78}{\sqrt{1.6084}}$ and $\frac{\sqrt{1.6084}}{\sqrt{1.6084}}$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

Raise $\sqrt{1.6084}$ to the power of $1$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

Raise $\sqrt{1.6084}$ to the power of $1$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

Apply the power rule $a^{m} a^{n} = a^{m + n}$ to Add exponents.

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{\sqrt{1.6084}}^{1 + 1}}$

Add $1$ and $1$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{\sqrt{1.6084}}^{2}}$

Should be rewritten ${\sqrt{1.6084}}^{2}$ as $1.6084$ .

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Rewrite $\sqrt{1.6084}$ as ${1.6084}^{\frac{1}{2}}$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{({1.6084}^{\frac{1}{2}})}^{2}}$

Use the power rule when multiplying the exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{1.6084}^{\frac{1}{2} \cdot 2}}$

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

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{1.6084}^{\frac{2}{2}}}$

The common factor should be canceled of $2$ .

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Cancel the common factor.

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{{1.6084}^{\frac{2}{2}}}$

First, divide $1$ by $1$ .

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{1.6084}$

Solve the exponent.

$\sin (A) = \frac{0.78 \sqrt{1.6084}}{1.6084}$

Multiply $0.78$ by $\sqrt{1.6084}$ .

$\sin (A) = \frac{0.98921714}{1.6084}$

Divide $0.98921714$ by $1.6084$ .

$\sin (A) = 0.61503179$

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.

$\cos (A) = \frac{1}{\sqrt{1.6084}}$

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

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Multiply $\frac{1}{\sqrt{1.6084}}$ by $\frac{\sqrt{1.6084}}{\sqrt{1.6084}}$ .

$\cos (A) = \frac{1}{\sqrt{1.6084}} \cdot \frac{\sqrt{1.6084}}{\sqrt{1.6084}}$

Add and then simplify the denominator.

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Multiply $\frac{1}{\sqrt{1.6084}}$ and $\frac{\sqrt{1.6084}}{\sqrt{1.6084}}$ .

$\cos (A) = \frac{\sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

Raise $\sqrt{1.6084}$ to the power of $1$ .

$\cos (A) = \frac{\sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

Raise $\sqrt{1.6084}$ to the power of $1$ .

$\cos (A) = \frac{\sqrt{1.6084}}{\sqrt{1.6084} \sqrt{1.6084}}$

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

$\cos (A) = \frac{\sqrt{1.6084}}{{\sqrt{1.6084}}^{1 + 1}}$

Add $1$ and $1$ .

$\cos (A) = \frac{\sqrt{1.6084}}{{\sqrt{1.6084}}^{2}}$

Rewrite ${\sqrt{1.6084}}^{2}$ as $1.6084$ .

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Rewrite $\sqrt{1.6084}$ as ${1.6084}^{\frac{1}{2}}$ .

$\cos (A) = \frac{\sqrt{1.6084}}{{({1.6084}^{\frac{1}{2}})}^{2}}$

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

$\cos (A) = \frac{\sqrt{1.6084}}{{1.6084}^{\frac{1}{2} \cdot 2}}$

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

$\cos (A) = \frac{\sqrt{1.6084}}{{1.6084}^{\frac{2}{2}}}$

The common factor $2$ should be canceled.

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Cancel the common factor.

$\cos (A) = \frac{\sqrt{1.6084}}{{1.6084}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\cos (A) = \frac{\sqrt{1.6084}}{1.6084}$

Evaluate the exponent.

$\cos (A) = \frac{\sqrt{1.6084}}{1.6084}$

Evaluate the root.

$\cos (A) = \frac{1.2682271}{1.6084}$

Divide $1.2682271$ by $1.6084$ .

$\cos (A) = 0.7885023$

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.

$\cot (A) = \frac{1}{0.78}$

Divide $1$ by $0.78$ .

$\cot (A) = 1.\overline{282051}$

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.

$\sec (A) = \frac{\sqrt{1.6084}}{1}$

Divide $\sqrt{1.6084}$ by $1$ .

$\sec (A) = \sqrt{1.6084}$

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.

$\csc (A) = \frac{\sqrt{1.6084}}{0.78}$

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

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Evaluate the root.

$\csc (A) = \frac{1.2682271}{0.78}$

Divide $1.2682271$ by $0.78$ .

$\csc (A) = 1.62593219$

This is the solution to each trig value.

$\sin (A) = 0.61503179$

$\cos (A) = 0.7885023$

$\tan (A) = 0.78$

$\cot (A) = 1.\overline{282051}$

$\sec (A) = \sqrt{1.6084}$

$\csc (A) = 1.62593219$

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