Sketching, Reference Angles, and Coterminal
Sketch the angle 370˚
Opening counterclockwise, all the way around one revolution ending in quadrant I.
What would be the length of the hypotenuse on a right triangle drawn using the coordinate (7, √26)?
5√3
What is 11π/5 in degrees?
396˚
Angle measures that sit on the x and y axes are called?
Quadrantals
Evaluate sin(765o)
sqrt(2)/2
In what quadrant is the angle 83π/15 located?
IV
The point (-3, 4) lies on the terminal side of an angle theta. What is the cosine of this angle?
costheta=-3/5
What is -1140˚ in radians (as a fraction in simplest form)?
-(19π)/3
Positive, acute angles that are measured nearest x-axis
Reference angles
Evaluate csc (-8π/3)
- (2sqrt(3))/3
Find the reference angle of -800 degrees
80 degrees
Given secθ = 9/2 and sinθ < 0, find cscθ.
(-9sqrt(77))/77
Ms. Murphy was eating a donut that had a diameter 11cm. The hole in the middle of the donut had a diameter of 6cm. Ms. Murphy took her first bite and (of course!) bit off a perfect piece that had a central angle of 80 degrees. What is the area of the piece of donut that Ms. Murphy ate?
(85π)/18 cm^2
A wind turbine has a pole from the ground to its center that is 460 feet tall with three 170ft blades. One blade is sticking out to the left and parallel to the ground. The blades rotate 404 degrees counterclockwise before coming to a stop. How high off the ground is the tip of the blade mentioned? Round to the nearest hundredth of a foot.
460-(170sin(44))=341.91 ft
Evaluate tan (9π/4)
1
Find one positive and one negative coterminal angle with least absolute value for
-(37π)/7
-(9π)/7 and (5π)/7
Given sinθ = -1/5 and cosθ < 0, find tanθ.
(sqrt(6))/12
What is -1140˚ in radians (as a fraction in simplest form)?
-19π/3
An ant on the ground sees the top of a garbage can at an angle of elevation of 21 degrees. He moves 10 inches closer to the garbage can to meet his friend and now looks at the top of the can at an angle of 45 degrees. How tall is the garbage can? Leave your answer in calculator ready form.
(10tan(21))/((tan(45)-tan(21)))*(tan(45))
Evaluate cot (-3π)
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