Question

find the angle between 0° and 360° that is coterminal to the given angle. 1010° let θ be the angle in standard position whose terminal side contains the given point. compute cos(θ) and sin(θ). answer exactly. (5,12) sin(θ)= cos(θ)=

Explanation:

Question 7

Step1: Divide the given angle by 360

To find the coterminal angle of \(1010^{\circ}\) between \(0^{\circ}\) and \(360^{\circ}\), we use the formula \(\theta - n\times360^{\circ}\), where \(n\) is an integer.
First, divide \(1010\) by \(360\): \(1010\div360 = 2\) (quotient) with a remainder. \(1010=360\times2 + 290\)

Answer:

\(290^{\circ}\)

Question 8

Step1: Find the radius \(r\)

For a point \((x,y)=(5,12)\) in the coordinate - plane, the radius \(r\) (distance from the origin \((0,0)\) to the point \((x,y)\)) is given by the formula \(r=\sqrt{x^{2}+y^{2}}\).
Substitute \(x = 5\) and \(y = 12\) into the formula: \(r=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\)

Step2: Calculate \(\sin\theta\) and \(\cos\theta\)

The definitions of \(\sin\theta\) and \(\cos\theta\) for an angle \(\theta\) in standard position with a point \((x,y)\) on its terminal side are \(\sin\theta=\frac{y}{r}\) and \(\cos\theta=\frac{x}{r}\)
Since \(x = 5\), \(y = 12\), and \(r = 13\)
\(\sin\theta=\frac{12}{13}\)
\(\cos\theta=\frac{5}{13}\)