Angle Properties & Unit Circle Basics
What is the reference angle of 120°?
60°
This reciprocal trigonometric ratio has a value of 2 when the angle is 60°
sec60
In a triangle, angle A is 77°, side a is 24.4 cm, and side b is 13.1 cm. This is the value of angle B, rounded to the nearest degree.
What is 32°?
A vertical cellular tower casts a shadow that is 20m long when the angle of elevation to the sun is exactly 60 degrees What is the exact height of the tower?
34.6m
Simplify: (sin^2 (θ) + cos^2 (θ)) / cos (θ)
sec (θ)
Give one positive coterminal angle of 45°.
405°
Evaluate: sin30 + cos60 + tan45
2
In a triangle, angle A is 65°, side b is 10.7 cm, and side c is 9.3 cm. This is the value of side length a.
What is 10.8 cm?
A surveyor needs to find the distance across a small pond between points A and B. They stand at a third point C where they can see both spots. They measure the distance AC = 50m, angle A = 40 degrees, angle C = 80 degrees. Which trigonometric tool should they use to find the direct distance AB.
sine law
Simplify: (1 - cos^2 (θ)) / sin (θ)
sin (θ)
What is the reference angle of 315°?
45°
Which exact value is found when 2cos45°sin45° is simplified?
1
In a triangle, side a is 14.8 cm, side b is 6.3 cm, and side c is 15.6 cm. These are the values of the angles, rounded to the nearest degree.
What are A = 71°, B = 24° and C = 85°?
Two straight roads diverge from an intersection at an angle of 60 degrees. A car travels 4 km down one road, and a bike travels 5 km down the other road. Find the direct distance d between the car and the bike.
4.58 km
Simplify: (sec^2 (θ) - 1) / tan (θ)
tan (θ)
This angle is coterminal with 585°, has a reference angle of 45°, and has trig ratios
225°
Which exact value is the result of (sin45°)(sin45°)+(sin30°)(sin60°)?
2+√3/4
In a triangle, angle A is 58°, side a is 17.9 cm and side b is 19.4 cm. These are the values of all possibilities for the remaining angle measures and the remaining side length, angles rounded to the nearest degree.
What are B1 = 67°, C1 = 55°, c1 = 17.3 cm, B2 = 113°, C2 = 9° and c2 = 3.3 cm?
A surveyor stands at point P and measures a diagonal line of sight to the top of a cliff T to be 50 m at an angle of elevation of 30 degrees. Further along the ground closer to the cliff, at a landmark L, the angle of elevation to the top of the cliff is 45 degrees, What is the exact length of the ground distance x between the surveyor P and the landmark L?
18.3m
Simplify: (sin (θ) / (1 + cos (θ))) +(sin (θ) / (1 - cos (θ)))
2csc (θ)
Find the two related angles between 0° and 360° if tan θ = -1.
135° and 315°
What simplified exact value is obtained from csc²60°-cot²30°
- 5/3
A surveyor is mapping a triangular piece of land. From point P, she measures the distance to point Q as 20.4 m. She then measures the distance from point P to point R as 15.2 m. The angle at point Q is found to be 40°. These are the values of all possibilities for the remaining angle measures and the remaining side length, angles rounded to the nearest degree.
What are R1 = 60°, P1 = 80°, p1 = 23.3 km, R2 = 120°, P2 = 20° and p2 = 8.1 km?
A vertical pole of height h casts a shadow on horizontal ground. Later in the day, the angle of elevation to the sun decreases by a known amount, causing the shadow to lengthen by x meters. If the two angles of elevation to the sun are A and B (where A > B), state the algebraic expression for the original length of the shadow using only x, A, and B.
xtan(B) / (tan(A) - tan(B)
Simplify: (sec (θ) - cos (θ)) / tan (θ)
sin (θ)