Question

find the value of each of the six trigonometric functions of the angle θ in the figure. a = 8 and b = 6 sinθ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expr

Explanation:

Step1: Find the hypotenuse \(c\)

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\). Given \(a = 8\) and \(b=6\), then \(c=\sqrt{8^{2}+6^{2}}=\sqrt{64 + 36}=\sqrt{100}=10\).

Step2: Calculate \(\sin\theta\)

The formula for \(\sin\theta\) in a right - triangle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to \(\theta\) is \(b = 6\) and the hypotenuse \(c = 10\). So \(\sin\theta=\frac{6}{10}=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\)