find cosθ, where θ is the angle shown. give an exact value, not a decimal approximation.
find cosθ, where θ is the angle shown. give an exact value, not a decimal approximation.
Answer
Explanation:
Step1: Find the hypotenuse
By the Pythagorean theorem (c=\sqrt{a^{2}+b^{2}}), where (a = 3) and (b=4). So (c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5).
Step2: Use the cosine - definition
The cosine of an angle (\theta) in a right - triangle is defined as (\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}). The adjacent side to (\theta) is 3 and the hypotenuse is 5. So (\cos\theta=\frac{3}{5}).
Answer:
(\frac{3}{5})