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find the six trigonometric function values of the specified angle.
cos θ = 5√74 / 74 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
tan θ = 7 / 5 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
sec θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
answer:
assuming the angle θ is opposite the side with length 5.
sin(θ)=5 / 13
cos(θ)=12 / 13
tan(θ)=5 / 12
csc(θ)=13 / 5
sec(θ)=13 / 12
cot(θ)=12 / 5
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Explanation:

Step1: Find hypotenuse

By Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 5$ and $b=7$. So $c=\sqrt{5^{2}+7^{2}}=\sqrt{25 + 49}=\sqrt{74}$.

Step2: Define sine

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{\sqrt{74}}=\frac{5\sqrt{74}}{74}$.

Step3: Define cosine

$\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{7}{\sqrt{74}}=\frac{7\sqrt{74}}{74}$.

Step4: Define tangent

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{5}{7}$.

Step5: Define cosecant

$\csc\theta=\frac{1}{\sin\theta}=\frac{\sqrt{74}}{5}$.

Step6: Define secant

$\sec\theta=\frac{1}{\cos\theta}=\frac{\sqrt{74}}{7}$.

Step7: Define cotangent

$\cot\theta=\frac{1}{\tan\theta}=\frac{7}{5}$.

Answer:

$\sin\theta=\frac{5\sqrt{74}}{74}$, $\cos\theta=\frac{7\sqrt{74}}{74}$, $\tan\theta=\frac{5}{7}$, $\csc\theta=\frac{\sqrt{74}}{5}$, $\sec\theta=\frac{\sqrt{74}}{7}$, $\cot\theta=\frac{7}{5}$