please help with these math question and explain how you got the anwser?
1.The point (3, -2) in on the terminal side of an angle t. Find cos(t) to 2 decimal places.
2.An angle with measure 5.6 radians is equal to how many degrees? Round your answer to 2 decimal places. Use 3.1416 as an approximation for pi.
3.In a circle of radius 20, find the length of the arc spanned by a central angle of pi/4 radians. Round your answer to 2 decimal places. Use 3.1416 as an approximation for pi.
Comments
➊ The point P(3, –2) in on the terminal side of an angle θ. Find cosθ to 2 decimal places.
Xp = 3, Yp = –2 ∴ r = √[3² + (–2)² ] =√13
∴ cos θ = x ÷ r = 3/√13 = 0.8320... = 0.83 (2 dp)
➋ An angle with measure 5.6 radians is equal to how many degrees? Round your answer to 2 decimal places. Use 3.1416 as an approximation for pi.
One rotation is 2π radians ≐ 6.283 radians = 360º
∴ 1 radian = 360/(2π) º = 180/π º
∴ 5.6 radians = 5.6 radians x 180/(π) º/radian = 5.6(180)/3.1416 = 320.855 ... º = 320.86º (2dp)
➌ In a circle of radius 20, find the length of the arc spanned by a central angle of π/4 = ¼π radians. Round your answer to 2 decimal places. Use 3.1416 as an approximation for pi.
arc length, a = r•θ where r is the circle's radius, and θ is the central angle (in radians)
∴ a = 20(¼π) = 5π units = 5(3.1416) = 15.708 = 15.71 units (2 dp)
.